Complex division, imag part

Percentage Accurate: 61.7% → 82.7%

Time: 7.4s

Alternatives: 11

Speedup: 1.1×

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: 61.7% 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: 82.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c \cdot b - a \cdot d\\ \mathbf{if}\;c \leq -3 \cdot 10^{+52}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-131}:\\ \;\;\;\;\frac{t\_0}{\mathsf{fma}\left(c, c, d \cdot d\right)}\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \mathbf{elif}\;c \leq 10^{+39}:\\ \;\;\;\;\frac{t\_0}{d \cdot d + c \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{-1}{\frac{\frac{c}{a}}{d}}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (* c b) (* a d))))
   (if (<= c -3e+52)
     (/ (- b (* a (/ d c))) c)
     (if (<= c -2.3e-131)
       (/ t_0 (fma c c (* d d)))
       (if (<= c 3.9e-91)
         (/ (- (/ (* c b) d) a) d)
         (if (<= c 1e+39)
           (/ t_0 (+ (* d d) (* c c)))
           (/ (+ b (/ -1.0 (/ (/ c a) d))) c)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (c * b) - (a * d);
	double tmp;
	if (c <= -3e+52) {
		tmp = (b - (a * (d / c))) / c;
	} else if (c <= -2.3e-131) {
		tmp = t_0 / fma(c, c, (d * d));
	} else if (c <= 3.9e-91) {
		tmp = (((c * b) / d) - a) / d;
	} else if (c <= 1e+39) {
		tmp = t_0 / ((d * d) + (c * c));
	} else {
		tmp = (b + (-1.0 / ((c / a) / d))) / c;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(c * b) - Float64(a * d))
	tmp = 0.0
	if (c <= -3e+52)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	elseif (c <= -2.3e-131)
		tmp = Float64(t_0 / fma(c, c, Float64(d * d)));
	elseif (c <= 3.9e-91)
		tmp = Float64(Float64(Float64(Float64(c * b) / d) - a) / d);
	elseif (c <= 1e+39)
		tmp = Float64(t_0 / Float64(Float64(d * d) + Float64(c * c)));
	else
		tmp = Float64(Float64(b + Float64(-1.0 / Float64(Float64(c / a) / d))) / c);
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(c * b), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3e+52], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, -2.3e-131], N[(t$95$0 / N[(c * c + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.9e-91], N[(N[(N[(N[(c * b), $MachinePrecision] / d), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 1e+39], N[(t$95$0 / N[(N[(d * d), $MachinePrecision] + N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b + N[(-1.0 / N[(N[(c / a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -3e52

   1. Initial program 45.2%

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

   3. Taylor expanded in c around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

      3. associate-/l* 89.0%

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

   5. Simplified 89.0%

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

   if -3e52 < c < -2.30000000000000022e-131

   1. Initial program 84.5%

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

      1. fma-define 84.5%

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

   3. Simplified 84.5%

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

   if -2.30000000000000022e-131 < c < 3.89999999999999994e-91

   1. Initial program 68.1%

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

   3. Taylor expanded in d around inf 93.0%

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

      1. frac-2neg 93.0%

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

      2. distribute-frac-neg2 93.0%

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

      3. distribute-neg-in 93.0%

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

      4. add-sqr-sqrt 48.8%

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

      5. sqrt-unprod 54.2%

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

      6. mul-1-neg 54.2%

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

      7. mul-1-neg 54.2%

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

      8. sqr-neg 54.2%

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

      9. sqrt-unprod 14.4%

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

      10. add-sqr-sqrt 31.9%

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

      11. mul-1-neg 31.9%

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

      12. sub-neg 31.9%

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

      13. add-sqr-sqrt 17.5%

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

      14. sqrt-unprod 52.5%

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

      15. mul-1-neg 52.5%

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

      16. mul-1-neg 52.5%

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

      17. sqr-neg 52.5%

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

      18. sqrt-unprod 43.8%

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

      19. add-sqr-sqrt 93.0%

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

      20. associate-/l* 92.0%

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

   5. Applied egg-rr 92.0%

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

   6. Taylor expanded in b around 0 93.0%

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

   if 3.89999999999999994e-91 < c < 9.9999999999999994e38

   1. Initial program 89.1%

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

   if 9.9999999999999994e38 < c

   1. Initial program 35.1%

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

   3. Taylor expanded in c around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

      1. associate-*r/ 73.4%

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

      2. clear-num 73.4%

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

      3. *-commutative 73.4%

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

   7. Applied egg-rr 73.4%

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

      1. *-un-lft-identity 73.4%

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

      2. *-commutative 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-/r* 78.6%

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

   9. Applied egg-rr 78.6%

      \[\leadsto \frac{b - \frac{1}{\color{blue}{\frac{\frac{c}{a}}{d} \cdot 1}}}{c} \]
3. Recombined 5 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3 \cdot 10^{+52}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-131}:\\ \;\;\;\;\frac{c \cdot b - a \cdot d}{\mathsf{fma}\left(c, c, d \cdot d\right)}\\ \mathbf{elif}\;c \leq 3.9 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \mathbf{elif}\;c \leq 10^{+39}:\\ \;\;\;\;\frac{c \cdot b - a \cdot d}{d \cdot d + c \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{-1}{\frac{\frac{c}{a}}{d}}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 82.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot b - a \cdot d}{d \cdot d + c \cdot c}\\ \mathbf{if}\;c \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-131}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \mathbf{elif}\;c \leq 10^{+39}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{-1}{\frac{\frac{c}{a}}{d}}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* c b) (* a d)) (+ (* d d) (* c c)))))
   (if (<= c -1.65e+50)
     (/ (- b (* a (/ d c))) c)
     (if (<= c -2.5e-131)
       t_0
       (if (<= c 3.4e-91)
         (/ (- (/ (* c b) d) a) d)
         (if (<= c 1e+39) t_0 (/ (+ b (/ -1.0 (/ (/ c a) d))) c)))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * b) - (a * d)) / ((d * d) + (c * c));
	double tmp;
	if (c <= -1.65e+50) {
		tmp = (b - (a * (d / c))) / c;
	} else if (c <= -2.5e-131) {
		tmp = t_0;
	} else if (c <= 3.4e-91) {
		tmp = (((c * b) / d) - a) / d;
	} else if (c <= 1e+39) {
		tmp = t_0;
	} else {
		tmp = (b + (-1.0 / ((c / a) / 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) :: t_0
    real(8) :: tmp
    t_0 = ((c * b) - (a * d)) / ((d * d) + (c * c))
    if (c <= (-1.65d+50)) then
        tmp = (b - (a * (d / c))) / c
    else if (c <= (-2.5d-131)) then
        tmp = t_0
    else if (c <= 3.4d-91) then
        tmp = (((c * b) / d) - a) / d
    else if (c <= 1d+39) then
        tmp = t_0
    else
        tmp = (b + ((-1.0d0) / ((c / a) / d))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * b) - (a * d)) / ((d * d) + (c * c));
	double tmp;
	if (c <= -1.65e+50) {
		tmp = (b - (a * (d / c))) / c;
	} else if (c <= -2.5e-131) {
		tmp = t_0;
	} else if (c <= 3.4e-91) {
		tmp = (((c * b) / d) - a) / d;
	} else if (c <= 1e+39) {
		tmp = t_0;
	} else {
		tmp = (b + (-1.0 / ((c / a) / d))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * b) - (a * d)) / ((d * d) + (c * c))
	tmp = 0
	if c <= -1.65e+50:
		tmp = (b - (a * (d / c))) / c
	elif c <= -2.5e-131:
		tmp = t_0
	elif c <= 3.4e-91:
		tmp = (((c * b) / d) - a) / d
	elif c <= 1e+39:
		tmp = t_0
	else:
		tmp = (b + (-1.0 / ((c / a) / d))) / c
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * b) - Float64(a * d)) / Float64(Float64(d * d) + Float64(c * c)))
	tmp = 0.0
	if (c <= -1.65e+50)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	elseif (c <= -2.5e-131)
		tmp = t_0;
	elseif (c <= 3.4e-91)
		tmp = Float64(Float64(Float64(Float64(c * b) / d) - a) / d);
	elseif (c <= 1e+39)
		tmp = t_0;
	else
		tmp = Float64(Float64(b + Float64(-1.0 / Float64(Float64(c / a) / d))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * b) - (a * d)) / ((d * d) + (c * c));
	tmp = 0.0;
	if (c <= -1.65e+50)
		tmp = (b - (a * (d / c))) / c;
	elseif (c <= -2.5e-131)
		tmp = t_0;
	elseif (c <= 3.4e-91)
		tmp = (((c * b) / d) - a) / d;
	elseif (c <= 1e+39)
		tmp = t_0;
	else
		tmp = (b + (-1.0 / ((c / a) / d))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * b), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(d * d), $MachinePrecision] + N[(c * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.65e+50], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, -2.5e-131], t$95$0, If[LessEqual[c, 3.4e-91], N[(N[(N[(N[(c * b), $MachinePrecision] / d), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[c, 1e+39], t$95$0, N[(N[(b + N[(-1.0 / N[(N[(c / a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.65e50

   1. Initial program 45.2%

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

   3. Taylor expanded in c around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. unsub-neg 82.4%

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

      3. associate-/l* 89.0%

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

   5. Simplified 89.0%

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

   if -1.65e50 < c < -2.5000000000000002e-131 or 3.40000000000000027e-91 < c < 9.9999999999999994e38

   1. Initial program 86.6%

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

   if -2.5000000000000002e-131 < c < 3.40000000000000027e-91

   1. Initial program 68.1%

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

   3. Taylor expanded in d around inf 93.0%

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

      1. frac-2neg 93.0%

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

      2. distribute-frac-neg2 93.0%

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

      3. distribute-neg-in 93.0%

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

      4. add-sqr-sqrt 48.8%

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

      5. sqrt-unprod 54.2%

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

      6. mul-1-neg 54.2%

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

      7. mul-1-neg 54.2%

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

      8. sqr-neg 54.2%

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

      9. sqrt-unprod 14.4%

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

      10. add-sqr-sqrt 31.9%

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

      11. mul-1-neg 31.9%

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

      12. sub-neg 31.9%

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

      13. add-sqr-sqrt 17.5%

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

      14. sqrt-unprod 52.5%

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

      15. mul-1-neg 52.5%

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

      16. mul-1-neg 52.5%

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

      17. sqr-neg 52.5%

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

      18. sqrt-unprod 43.8%

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

      19. add-sqr-sqrt 93.0%

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

      20. associate-/l* 92.0%

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

   5. Applied egg-rr 92.0%

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

   6. Taylor expanded in b around 0 93.0%

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

   if 9.9999999999999994e38 < c

   1. Initial program 35.1%

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

   3. Taylor expanded in c around inf 73.4%

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

      1. mul-1-neg 73.4%

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

      2. unsub-neg 73.4%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

      1. associate-*r/ 73.4%

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

      2. clear-num 73.4%

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

      3. *-commutative 73.4%

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

   7. Applied egg-rr 73.4%

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

      1. *-un-lft-identity 73.4%

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

      2. *-commutative 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-/r* 78.6%

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

   9. Applied egg-rr 78.6%

      \[\leadsto \frac{b - \frac{1}{\color{blue}{\frac{\frac{c}{a}}{d} \cdot 1}}}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.65 \cdot 10^{+50}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq -2.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{c \cdot b - a \cdot d}{d \cdot d + c \cdot c}\\ \mathbf{elif}\;c \leq 3.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \mathbf{elif}\;c \leq 10^{+39}:\\ \;\;\;\;\frac{c \cdot b - a \cdot d}{d \cdot d + c \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{-1}{\frac{\frac{c}{a}}{d}}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-57}:\\ \;\;\;\;\frac{\left(c \cdot b\right) \cdot \frac{1}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{1}{\frac{c}{d} \cdot \frac{-1}{a}}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -2e-14)
   (/ (- b (* a (/ d c))) c)
   (if (<= c 1.02e-57)
     (/ (- (* (* c b) (/ 1.0 d)) a) d)
     (/ (+ b (/ 1.0 (* (/ c d) (/ -1.0 a)))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -2e-14) {
		tmp = (b - (a * (d / c))) / c;
	} else if (c <= 1.02e-57) {
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	} else {
		tmp = (b + (1.0 / ((c / d) * (-1.0 / 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 (c <= (-2d-14)) then
        tmp = (b - (a * (d / c))) / c
    else if (c <= 1.02d-57) then
        tmp = (((c * b) * (1.0d0 / d)) - a) / d
    else
        tmp = (b + (1.0d0 / ((c / d) * ((-1.0d0) / a)))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -2e-14) {
		tmp = (b - (a * (d / c))) / c;
	} else if (c <= 1.02e-57) {
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	} else {
		tmp = (b + (1.0 / ((c / d) * (-1.0 / a)))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -2e-14:
		tmp = (b - (a * (d / c))) / c
	elif c <= 1.02e-57:
		tmp = (((c * b) * (1.0 / d)) - a) / d
	else:
		tmp = (b + (1.0 / ((c / d) * (-1.0 / a)))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -2e-14)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	elseif (c <= 1.02e-57)
		tmp = Float64(Float64(Float64(Float64(c * b) * Float64(1.0 / d)) - a) / d);
	else
		tmp = Float64(Float64(b + Float64(1.0 / Float64(Float64(c / d) * Float64(-1.0 / a)))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -2e-14)
		tmp = (b - (a * (d / c))) / c;
	elseif (c <= 1.02e-57)
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	else
		tmp = (b + (1.0 / ((c / d) * (-1.0 / a)))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -2e-14], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 1.02e-57], N[(N[(N[(N[(c * b), $MachinePrecision] * N[(1.0 / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], N[(N[(b + N[(1.0 / N[(N[(c / d), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -2e-14

   1. Initial program 56.0%

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

   3. Taylor expanded in c around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

   if -2e-14 < c < 1.02e-57

   1. Initial program 71.9%

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

   3. Taylor expanded in d around inf 87.6%

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

      1. div-inv 87.6%

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

      2. *-commutative 87.6%

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

   5. Applied egg-rr 87.6%

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

   if 1.02e-57 < c

   1. Initial program 47.9%

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

   3. Taylor expanded in c around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

      3. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

      1. associate-*r/ 69.6%

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

      2. clear-num 69.6%

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

      3. *-commutative 69.6%

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

   7. Applied egg-rr 69.6%

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

      1. associate-/r* 73.4%

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

      2. div-inv 73.4%

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

   9. Applied egg-rr 73.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2 \cdot 10^{-14}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-57}:\\ \;\;\;\;\frac{\left(c \cdot b\right) \cdot \frac{1}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{1}{\frac{c}{d} \cdot \frac{-1}{a}}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{-14} \lor \neg \left(c \leq 4.5 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(c \cdot b\right) \cdot \frac{1}{d} - a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.75e-14) (not (<= c 4.5e-58)))
   (/ (- b (* a (/ d c))) c)
   (/ (- (* (* c b) (/ 1.0 d)) a) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.75e-14) || !(c <= 4.5e-58)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = (((c * b) * (1.0 / d)) - a) / 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 <= (-2.75d-14)) .or. (.not. (c <= 4.5d-58))) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = (((c * b) * (1.0d0 / d)) - a) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.75e-14) || !(c <= 4.5e-58)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.75e-14) or not (c <= 4.5e-58):
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = (((c * b) * (1.0 / d)) - a) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.75e-14) || !(c <= 4.5e-58))
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = Float64(Float64(Float64(Float64(c * b) * Float64(1.0 / d)) - a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.75e-14) || ~((c <= 4.5e-58)))
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.75e-14], N[Not[LessEqual[c, 4.5e-58]], $MachinePrecision]], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(c * b), $MachinePrecision] * N[(1.0 / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.74999999999999996e-14 or 4.5000000000000003e-58 < c

   1. Initial program 51.3%

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

   3. Taylor expanded in c around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

   if -2.74999999999999996e-14 < c < 4.5000000000000003e-58

   1. Initial program 71.9%

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

   3. Taylor expanded in d around inf 87.6%

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

      1. div-inv 87.6%

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

      2. *-commutative 87.6%

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

   5. Applied egg-rr 87.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{-14} \lor \neg \left(c \leq 4.5 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(c \cdot b\right) \cdot \frac{1}{d} - a}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{-15} \lor \neg \left(c \leq 10^{-57}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{d}{c \cdot b}} - a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -4.1e-15) (not (<= c 1e-57)))
   (/ (- b (* a (/ d c))) c)
   (/ (- (/ 1.0 (/ d (* c b))) a) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4.1e-15) || !(c <= 1e-57)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = ((1.0 / (d / (c * b))) - a) / 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 <= (-4.1d-15)) .or. (.not. (c <= 1d-57))) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = ((1.0d0 / (d / (c * b))) - a) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4.1e-15) || !(c <= 1e-57)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = ((1.0 / (d / (c * b))) - a) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -4.1e-15) or not (c <= 1e-57):
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = ((1.0 / (d / (c * b))) - a) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -4.1e-15) || !(c <= 1e-57))
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = Float64(Float64(Float64(1.0 / Float64(d / Float64(c * b))) - a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -4.1e-15) || ~((c <= 1e-57)))
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = ((1.0 / (d / (c * b))) - a) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -4.1e-15], N[Not[LessEqual[c, 1e-57]], $MachinePrecision]], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(1.0 / N[(d / N[(c * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.10000000000000036e-15 or 9.99999999999999955e-58 < c

   1. Initial program 51.3%

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

   3. Taylor expanded in c around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

   if -4.10000000000000036e-15 < c < 9.99999999999999955e-58

   1. Initial program 71.9%

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

   3. Taylor expanded in d around inf 87.6%

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

      1. frac-2neg 87.6%

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

      2. distribute-frac-neg2 87.6%

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

      3. distribute-neg-in 87.6%

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

      4. add-sqr-sqrt 42.2%

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

      5. sqrt-unprod 51.8%

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

      6. mul-1-neg 51.8%

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

      7. mul-1-neg 51.8%

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

      8. sqr-neg 51.8%

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

      9. sqrt-unprod 18.9%

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

      10. add-sqr-sqrt 34.3%

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

      11. mul-1-neg 34.3%

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

      12. sub-neg 34.3%

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

      13. add-sqr-sqrt 15.4%

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

      14. sqrt-unprod 52.8%

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

      15. mul-1-neg 52.8%

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

      16. mul-1-neg 52.8%

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

      17. sqr-neg 52.8%

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

      18. sqrt-unprod 45.1%

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

      19. add-sqr-sqrt 87.6%

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

      20. associate-/l* 86.8%

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

   5. Applied egg-rr 86.8%

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

      1. associate-*r/ 87.6%

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

      2. clear-num 87.6%

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

   7. Applied egg-rr 87.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.1 \cdot 10^{-15} \lor \neg \left(c \leq 10^{-57}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\frac{d}{c \cdot b}} - a}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-57}:\\ \;\;\;\;\frac{\left(c \cdot b\right) \cdot \frac{1}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{-1}{\frac{\frac{c}{a}}{d}}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -4.6e-15)
   (/ (- b (* a (/ d c))) c)
   (if (<= c 1.02e-57)
     (/ (- (* (* c b) (/ 1.0 d)) a) d)
     (/ (+ b (/ -1.0 (/ (/ c a) d))) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -4.6e-15) {
		tmp = (b - (a * (d / c))) / c;
	} else if (c <= 1.02e-57) {
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	} else {
		tmp = (b + (-1.0 / ((c / a) / 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 (c <= (-4.6d-15)) then
        tmp = (b - (a * (d / c))) / c
    else if (c <= 1.02d-57) then
        tmp = (((c * b) * (1.0d0 / d)) - a) / d
    else
        tmp = (b + ((-1.0d0) / ((c / a) / d))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -4.6e-15) {
		tmp = (b - (a * (d / c))) / c;
	} else if (c <= 1.02e-57) {
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	} else {
		tmp = (b + (-1.0 / ((c / a) / d))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -4.6e-15:
		tmp = (b - (a * (d / c))) / c
	elif c <= 1.02e-57:
		tmp = (((c * b) * (1.0 / d)) - a) / d
	else:
		tmp = (b + (-1.0 / ((c / a) / d))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -4.6e-15)
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	elseif (c <= 1.02e-57)
		tmp = Float64(Float64(Float64(Float64(c * b) * Float64(1.0 / d)) - a) / d);
	else
		tmp = Float64(Float64(b + Float64(-1.0 / Float64(Float64(c / a) / d))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -4.6e-15)
		tmp = (b - (a * (d / c))) / c;
	elseif (c <= 1.02e-57)
		tmp = (((c * b) * (1.0 / d)) - a) / d;
	else
		tmp = (b + (-1.0 / ((c / a) / d))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -4.6e-15], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[c, 1.02e-57], N[(N[(N[(N[(c * b), $MachinePrecision] * N[(1.0 / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], N[(N[(b + N[(-1.0 / N[(N[(c / a), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.59999999999999981e-15

   1. Initial program 56.0%

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

   3. Taylor expanded in c around inf 80.4%

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

      1. mul-1-neg 80.4%

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

      2. unsub-neg 80.4%

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

      3. associate-/l* 85.5%

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

   5. Simplified 85.5%

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

   if -4.59999999999999981e-15 < c < 1.02e-57

   1. Initial program 71.9%

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

   3. Taylor expanded in d around inf 87.6%

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

      1. div-inv 87.6%

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

      2. *-commutative 87.6%

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

   5. Applied egg-rr 87.6%

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

   if 1.02e-57 < c

   1. Initial program 47.9%

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

   3. Taylor expanded in c around inf 69.6%

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

      1. mul-1-neg 69.6%

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

      2. unsub-neg 69.6%

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

      3. associate-/l* 73.3%

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

   5. Simplified 73.3%

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

      1. associate-*r/ 69.6%

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

      2. clear-num 69.6%

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

      3. *-commutative 69.6%

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

   7. Applied egg-rr 69.6%

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

      1. *-un-lft-identity 69.6%

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

      2. *-commutative 69.6%

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

      3. *-commutative 69.6%

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

      4. associate-/r* 73.4%

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

   9. Applied egg-rr 73.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{-15}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{elif}\;c \leq 1.02 \cdot 10^{-57}:\\ \;\;\;\;\frac{\left(c \cdot b\right) \cdot \frac{1}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \frac{-1}{\frac{\frac{c}{a}}{d}}}{c}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{-14} \lor \neg \left(c \leq 8.5 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.1e-14) (not (<= c 8.5e-58)))
   (/ (- b (* a (/ d c))) c)
   (/ (- (/ (* c b) d) a) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.1e-14) || !(c <= 8.5e-58)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = (((c * b) / d) - a) / 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 <= (-2.1d-14)) .or. (.not. (c <= 8.5d-58))) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = (((c * b) / d) - a) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.1e-14) || !(c <= 8.5e-58)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = (((c * b) / d) - a) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.1e-14) or not (c <= 8.5e-58):
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = (((c * b) / d) - a) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.1e-14) || !(c <= 8.5e-58))
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = Float64(Float64(Float64(Float64(c * b) / d) - a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.1e-14) || ~((c <= 8.5e-58)))
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = (((c * b) / d) - a) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.1e-14], N[Not[LessEqual[c, 8.5e-58]], $MachinePrecision]], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(N[(c * b), $MachinePrecision] / d), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.0999999999999999e-14 or 8.5000000000000004e-58 < c

   1. Initial program 51.3%

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

   3. Taylor expanded in c around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

   if -2.0999999999999999e-14 < c < 8.5000000000000004e-58

   1. Initial program 71.9%

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

   3. Taylor expanded in d around inf 87.6%

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

      1. frac-2neg 87.6%

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

      2. distribute-frac-neg2 87.6%

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

      3. distribute-neg-in 87.6%

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

      4. add-sqr-sqrt 42.2%

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

      5. sqrt-unprod 51.8%

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

      6. mul-1-neg 51.8%

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

      7. mul-1-neg 51.8%

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

      8. sqr-neg 51.8%

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

      9. sqrt-unprod 18.9%

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

      10. add-sqr-sqrt 34.3%

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

      11. mul-1-neg 34.3%

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

      12. sub-neg 34.3%

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

      13. add-sqr-sqrt 15.4%

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

      14. sqrt-unprod 52.8%

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

      15. mul-1-neg 52.8%

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

      16. mul-1-neg 52.8%

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

      17. sqr-neg 52.8%

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

      18. sqrt-unprod 45.1%

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

      19. add-sqr-sqrt 87.6%

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

      20. associate-/l* 86.8%

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

   5. Applied egg-rr 86.8%

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

   6. Taylor expanded in b around 0 87.6%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.1 \cdot 10^{-14} \lor \neg \left(c \leq 8.5 \cdot 10^{-58}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d} - a}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-14} \lor \neg \left(c \leq 1.02 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -1.9e-14) (not (<= c 1.02e-57)))
   (/ (- b (* a (/ d c))) c)
   (/ (- (* b (/ c d)) a) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.9e-14) || !(c <= 1.02e-57)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = ((b * (c / d)) - a) / 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 <= (-1.9d-14)) .or. (.not. (c <= 1.02d-57))) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = ((b * (c / d)) - a) / d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -1.9e-14) || !(c <= 1.02e-57)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = ((b * (c / d)) - a) / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -1.9e-14) or not (c <= 1.02e-57):
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = ((b * (c / d)) - a) / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -1.9e-14) || !(c <= 1.02e-57))
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = Float64(Float64(Float64(b * Float64(c / d)) - a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -1.9e-14) || ~((c <= 1.02e-57)))
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = ((b * (c / d)) - a) / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -1.9e-14], N[Not[LessEqual[c, 1.02e-57]], $MachinePrecision]], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(N[(N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.9000000000000001e-14 or 1.02e-57 < c

   1. Initial program 51.3%

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

   3. Taylor expanded in c around inf 74.1%

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

      1. mul-1-neg 74.1%

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

      2. unsub-neg 74.1%

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

      3. associate-/l* 78.5%

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

   5. Simplified 78.5%

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

   if -1.9000000000000001e-14 < c < 1.02e-57

   1. Initial program 71.9%

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

   3. Taylor expanded in d around inf 87.6%

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

      1. frac-2neg 87.6%

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

      2. distribute-frac-neg2 87.6%

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

      3. distribute-neg-in 87.6%

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

      4. add-sqr-sqrt 42.2%

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

      5. sqrt-unprod 51.8%

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

      6. mul-1-neg 51.8%

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

      7. mul-1-neg 51.8%

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

      8. sqr-neg 51.8%

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

      9. sqrt-unprod 18.9%

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

      10. add-sqr-sqrt 34.3%

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

      11. mul-1-neg 34.3%

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

      12. sub-neg 34.3%

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

      13. add-sqr-sqrt 15.4%

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

      14. sqrt-unprod 52.8%

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

      15. mul-1-neg 52.8%

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

      16. mul-1-neg 52.8%

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

      17. sqr-neg 52.8%

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

      18. sqrt-unprod 45.1%

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

      19. add-sqr-sqrt 87.6%

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

      20. associate-/l* 86.8%

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

   5. Applied egg-rr 86.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.9 \cdot 10^{-14} \lor \neg \left(c \leq 1.02 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b \cdot \frac{c}{d} - a}{d}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-15} \lor \neg \left(c \leq 6.5 \cdot 10^{-107}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -3.5e-15) (not (<= c 6.5e-107)))
   (/ (- b (* a (/ d c))) c)
   (/ a (- d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -3.5e-15) || !(c <= 6.5e-107)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = a / -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 <= (-3.5d-15)) .or. (.not. (c <= 6.5d-107))) then
        tmp = (b - (a * (d / c))) / c
    else
        tmp = a / -d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -3.5e-15) || !(c <= 6.5e-107)) {
		tmp = (b - (a * (d / c))) / c;
	} else {
		tmp = a / -d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -3.5e-15) or not (c <= 6.5e-107):
		tmp = (b - (a * (d / c))) / c
	else:
		tmp = a / -d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -3.5e-15) || !(c <= 6.5e-107))
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	else
		tmp = Float64(a / Float64(-d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -3.5e-15) || ~((c <= 6.5e-107)))
		tmp = (b - (a * (d / c))) / c;
	else
		tmp = a / -d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -3.5e-15], N[Not[LessEqual[c, 6.5e-107]], $MachinePrecision]], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(a / (-d)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -3.5000000000000001e-15 or 6.5000000000000002e-107 < c

   1. Initial program 54.3%

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

   3. Taylor expanded in c around inf 71.8%

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

      1. mul-1-neg 71.8%

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

      2. unsub-neg 71.8%

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

      3. associate-/l* 75.8%

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

   5. Simplified 75.8%

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

   if -3.5000000000000001e-15 < c < 6.5000000000000002e-107

   1. Initial program 70.3%

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

   3. Taylor expanded in c around 0 72.3%

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

      1. associate-*r/ 72.3%

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

      2. mul-1-neg 72.3%

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

   5. Simplified 72.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.5 \cdot 10^{-15} \lor \neg \left(c \leq 6.5 \cdot 10^{-107}\right):\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-d}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{-14} \lor \neg \left(c \leq 2 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -2.75e-14) (not (<= c 2e-90))) (/ b c) (/ a (- d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.75e-14) || !(c <= 2e-90)) {
		tmp = b / c;
	} else {
		tmp = a / -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 <= (-2.75d-14)) .or. (.not. (c <= 2d-90))) then
        tmp = b / c
    else
        tmp = a / -d
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -2.75e-14) || !(c <= 2e-90)) {
		tmp = b / c;
	} else {
		tmp = a / -d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -2.75e-14) or not (c <= 2e-90):
		tmp = b / c
	else:
		tmp = a / -d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -2.75e-14) || !(c <= 2e-90))
		tmp = Float64(b / c);
	else
		tmp = Float64(a / Float64(-d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -2.75e-14) || ~((c <= 2e-90)))
		tmp = b / c;
	else
		tmp = a / -d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -2.75e-14], N[Not[LessEqual[c, 2e-90]], $MachinePrecision]], N[(b / c), $MachinePrecision], N[(a / (-d)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.74999999999999996e-14 or 1.99999999999999999e-90 < c

   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 inf 63.1%

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

   if -2.74999999999999996e-14 < c < 1.99999999999999999e-90

   1. Initial program 70.0%

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

   3. Taylor expanded in c around 0 71.0%

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

      1. associate-*r/ 71.0%

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

      2. mul-1-neg 71.0%

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

   5. Simplified 71.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.75 \cdot 10^{-14} \lor \neg \left(c \leq 2 \cdot 10^{-90}\right):\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{-d}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 43.1% 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 61.0%

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

3. Taylor expanded in c around inf 40.5%

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

Developer target: 99.3% accurate, 0.1× speedup

Math

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

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 2024118 
(FPCore (a b c d)
  :name "Complex division, imag part"
  :precision binary64

  :alt
  (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))))