Complex division, imag part

Percentage Accurate: 61.3% → 89.3%

Time: 8.2s

Alternatives: 9

Speedup: 1.8×

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: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{\mathsf{hypot}\left(c, d\right)}\\ t_1 := b \cdot c - a \cdot d\\ \mathbf{if}\;\frac{t_1}{c \cdot c + d \cdot d} \leq 4 \cdot 10^{+288}:\\ \;\;\;\;t_0 \cdot \frac{t_1}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{c}{\frac{\mathsf{hypot}\left(c, d\right)}{b}} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ 1.0 (hypot c d))) (t_1 (- (* b c) (* a d))))
   (if (<= (/ t_1 (+ (* c c) (* d d))) 4e+288)
     (* t_0 (/ t_1 (hypot c d)))
     (- (* t_0 (/ c (/ (hypot c d) b))) (/ a d)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = 1.0 / hypot(c, d);
	double t_1 = (b * c) - (a * d);
	double tmp;
	if ((t_1 / ((c * c) + (d * d))) <= 4e+288) {
		tmp = t_0 * (t_1 / hypot(c, d));
	} else {
		tmp = (t_0 * (c / (hypot(c, d) / b))) - (a / d);
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = 1.0 / Math.hypot(c, d);
	double t_1 = (b * c) - (a * d);
	double tmp;
	if ((t_1 / ((c * c) + (d * d))) <= 4e+288) {
		tmp = t_0 * (t_1 / Math.hypot(c, d));
	} else {
		tmp = (t_0 * (c / (Math.hypot(c, d) / b))) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = 1.0 / math.hypot(c, d)
	t_1 = (b * c) - (a * d)
	tmp = 0
	if (t_1 / ((c * c) + (d * d))) <= 4e+288:
		tmp = t_0 * (t_1 / math.hypot(c, d))
	else:
		tmp = (t_0 * (c / (math.hypot(c, d) / b))) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(1.0 / hypot(c, d))
	t_1 = Float64(Float64(b * c) - Float64(a * d))
	tmp = 0.0
	if (Float64(t_1 / Float64(Float64(c * c) + Float64(d * d))) <= 4e+288)
		tmp = Float64(t_0 * Float64(t_1 / hypot(c, d)));
	else
		tmp = Float64(Float64(t_0 * Float64(c / Float64(hypot(c, d) / b))) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = 1.0 / hypot(c, d);
	t_1 = (b * c) - (a * d);
	tmp = 0.0;
	if ((t_1 / ((c * c) + (d * d))) <= 4e+288)
		tmp = t_0 * (t_1 / hypot(c, d));
	else
		tmp = (t_0 * (c / (hypot(c, d) / b))) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e+288], N[(t$95$0 * N[(t$95$1 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 * N[(c / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d))) < 4e288

   1. Initial program 78.8%

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

      1. *-un-lft-identity 78.8%

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

      2. add-sqr-sqrt 78.8%

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

      3. times-frac 78.7%

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

      4. hypot-def 78.7%

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

      5. hypot-def 95.8%

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

   3. Applied egg-rr 95.8%

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

   if 4e288 < (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 8.0%

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

      1. div-sub 4.9%

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

      2. *-un-lft-identity 4.9%

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

      3. add-sqr-sqrt 4.9%

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

      4. times-frac 4.9%

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

      5. fma-neg 4.9%

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

      6. hypot-def 4.9%

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

      7. hypot-def 7.6%

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

      8. associate-/l* 16.3%

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

      9. add-sqr-sqrt 16.3%

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

      10. pow2 16.3%

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

      11. hypot-def 16.3%

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

   3. Applied egg-rr 16.3%

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

      1. fma-neg 16.3%

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

      2. *-commutative 16.3%

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

      3. associate-/l* 61.8%

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

      4. associate-/l* 47.3%

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

      5. *-commutative 47.3%

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

      6. associate-/l* 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in d around inf 77.4%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \leq 4 \cdot 10^{+288}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{b \cdot c - a \cdot d}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{c}{\frac{\mathsf{hypot}\left(c, d\right)}{b}} - \frac{a}{d}\\ \end{array} \]

Alternative 2: 85.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := b \cdot c - a \cdot d\\ \mathbf{if}\;\frac{t_0}{c \cdot c + d \cdot d} \leq 4 \cdot 10^{+288}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{t_0}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{d} \cdot \frac{b}{d} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (* b c) (* a d))))
   (if (<= (/ t_0 (+ (* c c) (* d d))) 4e+288)
     (* (/ 1.0 (hypot c d)) (/ t_0 (hypot c d)))
     (- (* (/ c d) (/ b d)) (/ a d)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b * c) - (a * d);
	double tmp;
	if ((t_0 / ((c * c) + (d * d))) <= 4e+288) {
		tmp = (1.0 / hypot(c, d)) * (t_0 / hypot(c, d));
	} else {
		tmp = ((c / d) * (b / d)) - (a / d);
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (b * c) - (a * d);
	double tmp;
	if ((t_0 / ((c * c) + (d * d))) <= 4e+288) {
		tmp = (1.0 / Math.hypot(c, d)) * (t_0 / Math.hypot(c, d));
	} else {
		tmp = ((c / d) * (b / d)) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b * c) - (a * d)
	tmp = 0
	if (t_0 / ((c * c) + (d * d))) <= 4e+288:
		tmp = (1.0 / math.hypot(c, d)) * (t_0 / math.hypot(c, d))
	else:
		tmp = ((c / d) * (b / d)) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b * c) - Float64(a * d))
	tmp = 0.0
	if (Float64(t_0 / Float64(Float64(c * c) + Float64(d * d))) <= 4e+288)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(t_0 / hypot(c, d)));
	else
		tmp = Float64(Float64(Float64(c / d) * Float64(b / d)) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b * c) - (a * d);
	tmp = 0.0;
	if ((t_0 / ((c * c) + (d * d))) <= 4e+288)
		tmp = (1.0 / hypot(c, d)) * (t_0 / hypot(c, d));
	else
		tmp = ((c / d) * (b / d)) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$0 / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 4e+288], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(t$95$0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(c / d), $MachinePrecision] * N[(b / d), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d))) < 4e288

   1. Initial program 78.8%

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

      1. *-un-lft-identity 78.8%

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

      2. add-sqr-sqrt 78.8%

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

      3. times-frac 78.7%

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

      4. hypot-def 78.7%

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

      5. hypot-def 95.8%

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

   3. Applied egg-rr 95.8%

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

   if 4e288 < (/.f64 (-.f64 (*.f64 b c) (*.f64 a d)) (+.f64 (*.f64 c c) (*.f64 d d)))

   1. Initial program 8.0%

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

   2. Taylor expanded in c around 0 45.2%

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

      1. +-commutative 45.2%

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

      2. mul-1-neg 45.2%

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

      3. unsub-neg 45.2%

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

      4. unpow2 45.2%

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

      5. times-frac 63.2%

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

   4. Simplified 63.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \leq 4 \cdot 10^{+288}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{b \cdot c - a \cdot d}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{d} \cdot \frac{b}{d} - \frac{a}{d}\\ \end{array} \]

Alternative 3: 78.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c}{d} \cdot \frac{b}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -1.16 \cdot 10^{+63}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -1.65 \cdot 10^{-133}:\\ \;\;\;\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (* (/ c d) (/ b d)) (/ a d))))
   (if (<= d -1.16e+63)
     t_0
     (if (<= d -1.65e-133)
       (/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
       (if (<= d 2e+99) (/ (- b (/ a (/ c d))) c) t_0)))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c / d) * (b / d)) - (a / d);
	double tmp;
	if (d <= -1.16e+63) {
		tmp = t_0;
	} else if (d <= -1.65e-133) {
		tmp = ((b * c) - (a * d)) / ((c * c) + (d * d));
	} else if (d <= 2e+99) {
		tmp = (b - (a / (c / d))) / 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 / d) * (b / d)) - (a / d)
    if (d <= (-1.16d+63)) then
        tmp = t_0
    else if (d <= (-1.65d-133)) then
        tmp = ((b * c) - (a * d)) / ((c * c) + (d * d))
    else if (d <= 2d+99) then
        tmp = (b - (a / (c / d))) / 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 / d) * (b / d)) - (a / d);
	double tmp;
	if (d <= -1.16e+63) {
		tmp = t_0;
	} else if (d <= -1.65e-133) {
		tmp = ((b * c) - (a * d)) / ((c * c) + (d * d));
	} else if (d <= 2e+99) {
		tmp = (b - (a / (c / d))) / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c / d) * (b / d)) - (a / d)
	tmp = 0
	if d <= -1.16e+63:
		tmp = t_0
	elif d <= -1.65e-133:
		tmp = ((b * c) - (a * d)) / ((c * c) + (d * d))
	elif d <= 2e+99:
		tmp = (b - (a / (c / d))) / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c / d) * Float64(b / d)) - Float64(a / d))
	tmp = 0.0
	if (d <= -1.16e+63)
		tmp = t_0;
	elseif (d <= -1.65e-133)
		tmp = Float64(Float64(Float64(b * c) - Float64(a * d)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 2e+99)
		tmp = Float64(Float64(b - Float64(a / Float64(c / d))) / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c / d) * (b / d)) - (a / d);
	tmp = 0.0;
	if (d <= -1.16e+63)
		tmp = t_0;
	elseif (d <= -1.65e-133)
		tmp = ((b * c) - (a * d)) / ((c * c) + (d * d));
	elseif (d <= 2e+99)
		tmp = (b - (a / (c / d))) / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c / d), $MachinePrecision] * N[(b / d), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.16e+63], t$95$0, If[LessEqual[d, -1.65e-133], N[(N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2e+99], N[(N[(b - N[(a / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if d < -1.15999999999999994e63 or 1.9999999999999999e99 < d

   1. Initial program 39.5%

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

   2. Taylor expanded in c around 0 76.4%

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

      1. +-commutative 76.4%

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

      2. mul-1-neg 76.4%

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

      3. unsub-neg 76.4%

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

      4. unpow2 76.4%

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

      5. times-frac 89.4%

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

   4. Simplified 89.4%

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

   if -1.15999999999999994e63 < d < -1.65000000000000005e-133

   1. Initial program 92.1%

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

   if -1.65000000000000005e-133 < d < 1.9999999999999999e99

   1. Initial program 67.9%

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

   2. Taylor expanded in c around inf 75.7%

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

      1. +-commutative 75.7%

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

      2. mul-1-neg 75.7%

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

      3. unsub-neg 75.7%

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

      4. unpow2 75.7%

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

      5. times-frac 79.2%

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

   4. Simplified 79.2%

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

      1. associate-*r/ 80.0%

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

      2. sub-div 81.0%

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

   6. Applied egg-rr 81.0%

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

   7. Taylor expanded in a around 0 85.4%

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

      1. associate-/l* 85.5%

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

   9. Simplified 85.5%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.16 \cdot 10^{+63}:\\ \;\;\;\;\frac{c}{d} \cdot \frac{b}{d} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -1.65 \cdot 10^{-133}:\\ \;\;\;\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 2 \cdot 10^{+99}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{d} \cdot \frac{b}{d} - \frac{a}{d}\\ \end{array} \]

Alternative 4: 76.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.85 \cdot 10^{-31} \lor \neg \left(d \leq 2.8 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{c}{d} \cdot \frac{b}{d} - \frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.85e-31) (not (<= d 2.8e+99)))
   (- (* (/ c d) (/ b d)) (/ a d))
   (/ (- b (/ a (/ c d))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.85e-31) || !(d <= 2.8e+99)) {
		tmp = ((c / d) * (b / d)) - (a / d);
	} else {
		tmp = (b - (a / (c / d))) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-1.85d-31)) .or. (.not. (d <= 2.8d+99))) then
        tmp = ((c / d) * (b / d)) - (a / d)
    else
        tmp = (b - (a / (c / d))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.85e-31) || !(d <= 2.8e+99)) {
		tmp = ((c / d) * (b / d)) - (a / d);
	} else {
		tmp = (b - (a / (c / d))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.85e-31) or not (d <= 2.8e+99):
		tmp = ((c / d) * (b / d)) - (a / d)
	else:
		tmp = (b - (a / (c / d))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.85e-31) || !(d <= 2.8e+99))
		tmp = Float64(Float64(Float64(c / d) * Float64(b / d)) - Float64(a / d));
	else
		tmp = Float64(Float64(b - Float64(a / Float64(c / d))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -1.85e-31) || ~((d <= 2.8e+99)))
		tmp = ((c / d) * (b / d)) - (a / d);
	else
		tmp = (b - (a / (c / d))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -1.85e-31], N[Not[LessEqual[d, 2.8e+99]], $MachinePrecision]], N[(N[(N[(c / d), $MachinePrecision] * N[(b / d), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], N[(N[(b - N[(a / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -1.8499999999999999e-31 or 2.8e99 < d

   1. Initial program 45.7%

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

   2. Taylor expanded in c around 0 77.0%

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

      1. +-commutative 77.0%

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

      2. mul-1-neg 77.0%

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

      3. unsub-neg 77.0%

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

      4. unpow2 77.0%

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

      5. times-frac 88.3%

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

   4. Simplified 88.3%

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

   if -1.8499999999999999e-31 < d < 2.8e99

   1. Initial program 73.4%

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

   2. Taylor expanded in c around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. unpow2 73.8%

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

      5. times-frac 76.1%

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

   4. Simplified 76.1%

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

      1. associate-*r/ 76.8%

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

      2. sub-div 77.6%

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

   6. Applied egg-rr 77.6%

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

   7. Taylor expanded in a around 0 81.8%

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

      1. associate-/l* 81.9%

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

   9. Simplified 81.9%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.85 \cdot 10^{-31} \lor \neg \left(d \leq 2.8 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{c}{d} \cdot \frac{b}{d} - \frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \end{array} \]

Alternative 5: 71.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.5 \cdot 10^{-25} \lor \neg \left(d \leq 1.92 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.5e-25) (not (<= d 1.92e+99)))
   (/ (- a) d)
   (/ (- b (* a (/ d c))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.5e-25) || !(d <= 1.92e+99)) {
		tmp = -a / d;
	} else {
		tmp = (b - (a * (d / c))) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-1.5d-25)) .or. (.not. (d <= 1.92d+99))) then
        tmp = -a / d
    else
        tmp = (b - (a * (d / c))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.5e-25) || !(d <= 1.92e+99)) {
		tmp = -a / d;
	} else {
		tmp = (b - (a * (d / c))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.5e-25) or not (d <= 1.92e+99):
		tmp = -a / d
	else:
		tmp = (b - (a * (d / c))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.5e-25) || !(d <= 1.92e+99))
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -1.5e-25) || ~((d <= 1.92e+99)))
		tmp = -a / d;
	else
		tmp = (b - (a * (d / c))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -1.5e-25], N[Not[LessEqual[d, 1.92e+99]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -1.4999999999999999e-25 or 1.9199999999999999e99 < d

   1. Initial program 45.7%

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

   2. Taylor expanded in c around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   4. Simplified 76.8%

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

   if -1.4999999999999999e-25 < d < 1.9199999999999999e99

   1. Initial program 73.4%

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

   2. Taylor expanded in c around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. unpow2 73.8%

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

      5. times-frac 76.1%

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

   4. Simplified 76.1%

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

   5. Taylor expanded in b around 0 73.8%

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

      1. +-commutative 73.8%

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

      2. associate-*r/ 73.8%

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

      3. *-commutative 73.8%

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

      4. neg-mul-1 73.8%

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

      5. distribute-frac-neg 73.8%

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

      6. unpow2 73.8%

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

      7. times-frac 76.1%

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

      8. *-commutative 76.1%

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

      9. unsub-neg 76.1%

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

      10. associate-*l/ 80.3%

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

      11. div-sub 81.8%

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

   7. Simplified 81.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -1.5 \cdot 10^{-25} \lor \neg \left(d \leq 1.92 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c}\\ \end{array} \]

Alternative 6: 71.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -2.05 \cdot 10^{-26} \lor \neg \left(d \leq 2.05 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -2.05e-26) (not (<= d 2.05e+99)))
   (/ (- a) d)
   (/ (- b (/ a (/ c d))) c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -2.05e-26) || !(d <= 2.05e+99)) {
		tmp = -a / d;
	} else {
		tmp = (b - (a / (c / d))) / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-2.05d-26)) .or. (.not. (d <= 2.05d+99))) then
        tmp = -a / d
    else
        tmp = (b - (a / (c / d))) / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -2.05e-26) || !(d <= 2.05e+99)) {
		tmp = -a / d;
	} else {
		tmp = (b - (a / (c / d))) / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -2.05e-26) or not (d <= 2.05e+99):
		tmp = -a / d
	else:
		tmp = (b - (a / (c / d))) / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -2.05e-26) || !(d <= 2.05e+99))
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(Float64(b - Float64(a / Float64(c / d))) / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -2.05e-26) || ~((d <= 2.05e+99)))
		tmp = -a / d;
	else
		tmp = (b - (a / (c / d))) / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -2.05e-26], N[Not[LessEqual[d, 2.05e+99]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(N[(b - N[(a / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -2.0499999999999999e-26 or 2.0499999999999999e99 < d

   1. Initial program 45.7%

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

   2. Taylor expanded in c around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. neg-mul-1 76.8%

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

   4. Simplified 76.8%

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

   if -2.0499999999999999e-26 < d < 2.0499999999999999e99

   1. Initial program 73.4%

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

   2. Taylor expanded in c around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

      4. unpow2 73.8%

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

      5. times-frac 76.1%

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

   4. Simplified 76.1%

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

      1. associate-*r/ 76.8%

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

      2. sub-div 77.6%

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

   6. Applied egg-rr 77.6%

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

   7. Taylor expanded in a around 0 81.8%

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

      1. associate-/l* 81.9%

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

   9. Simplified 81.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -2.05 \cdot 10^{-26} \lor \neg \left(d \leq 2.05 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \end{array} \]

Alternative 7: 72.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -3.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{-a}{d + \frac{c \cdot c}{d}}\\ \mathbf{elif}\;d \leq 1.92 \cdot 10^{+99}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -3.5e-64)
   (/ (- a) (+ d (/ (* c c) d)))
   (if (<= d 1.92e+99) (/ (- b (/ a (/ c d))) c) (/ (- a) d))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -3.5e-64) {
		tmp = -a / (d + ((c * c) / d));
	} else if (d <= 1.92e+99) {
		tmp = (b - (a / (c / d))) / 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 (d <= (-3.5d-64)) then
        tmp = -a / (d + ((c * c) / d))
    else if (d <= 1.92d+99) then
        tmp = (b - (a / (c / d))) / 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 (d <= -3.5e-64) {
		tmp = -a / (d + ((c * c) / d));
	} else if (d <= 1.92e+99) {
		tmp = (b - (a / (c / d))) / c;
	} else {
		tmp = -a / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -3.5e-64:
		tmp = -a / (d + ((c * c) / d))
	elif d <= 1.92e+99:
		tmp = (b - (a / (c / d))) / c
	else:
		tmp = -a / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -3.5e-64)
		tmp = Float64(Float64(-a) / Float64(d + Float64(Float64(c * c) / d)));
	elseif (d <= 1.92e+99)
		tmp = Float64(Float64(b - Float64(a / Float64(c / d))) / c);
	else
		tmp = Float64(Float64(-a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -3.5e-64)
		tmp = -a / (d + ((c * c) / d));
	elseif (d <= 1.92e+99)
		tmp = (b - (a / (c / d))) / c;
	else
		tmp = -a / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -3.5e-64], N[((-a) / N[(d + N[(N[(c * c), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 1.92e+99], N[(N[(b - N[(a / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[((-a) / d), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if d < -3.5000000000000003e-64

   1. Initial program 57.0%

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

      1. *-un-lft-identity 57.0%

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

      2. add-sqr-sqrt 57.0%

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

      3. times-frac 57.0%

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

      4. hypot-def 57.0%

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

      5. hypot-def 70.6%

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

   3. Applied egg-rr 70.6%

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

   4. Taylor expanded in b around 0 51.9%

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

      1. mul-1-neg 51.9%

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

      2. associate-/l* 56.5%

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

      3. distribute-neg-frac 56.5%

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

      4. unpow2 56.5%

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

      5. unpow2 56.5%

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

      6. fma-def 56.6%

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

   6. Simplified 56.6%

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

   7. Taylor expanded in d around 0 78.7%

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

      1. +-commutative 78.7%

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

      2. unpow2 78.7%

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

   9. Simplified 78.7%

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

   if -3.5000000000000003e-64 < d < 1.9199999999999999e99

   1. Initial program 73.4%

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

   2. Taylor expanded in c around inf 74.4%

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

      1. +-commutative 74.4%

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

      2. mul-1-neg 74.4%

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

      3. unsub-neg 74.4%

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

      4. unpow2 74.4%

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

      5. times-frac 76.8%

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

   4. Simplified 76.8%

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

      1. associate-*r/ 77.5%

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

      2. sub-div 78.3%

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

   6. Applied egg-rr 78.3%

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

   7. Taylor expanded in a around 0 82.6%

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

      1. associate-/l* 82.7%

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

   9. Simplified 82.7%

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

   if 1.9199999999999999e99 < d

   1. Initial program 32.8%

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

   2. Taylor expanded in c around 0 76.0%

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

      1. associate-*r/ 76.0%

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

      2. neg-mul-1 76.0%

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

   4. Simplified 76.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -3.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{-a}{d + \frac{c \cdot c}{d}}\\ \mathbf{elif}\;d \leq 1.92 \cdot 10^{+99}:\\ \;\;\;\;\frac{b - \frac{a}{\frac{c}{d}}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{d}\\ \end{array} \]

Alternative 8: 62.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -3.2 \cdot 10^{-64} \lor \neg \left(d \leq 1.92 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -3.2e-64) (not (<= d 1.92e+99))) (/ (- a) d) (/ b c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.2e-64) || !(d <= 1.92e+99)) {
		tmp = -a / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-3.2d-64)) .or. (.not. (d <= 1.92d+99))) then
        tmp = -a / d
    else
        tmp = b / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -3.2e-64) || !(d <= 1.92e+99)) {
		tmp = -a / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -3.2e-64) or not (d <= 1.92e+99):
		tmp = -a / d
	else:
		tmp = b / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -3.2e-64) || !(d <= 1.92e+99))
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(b / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -3.2e-64) || ~((d <= 1.92e+99)))
		tmp = -a / d;
	else
		tmp = b / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -3.2e-64], N[Not[LessEqual[d, 1.92e+99]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(b / c), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if d < -3.19999999999999975e-64 or 1.9199999999999999e99 < d

   1. Initial program 46.6%

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

   2. Taylor expanded in c around 0 75.5%

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

      1. associate-*r/ 75.5%

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

      2. neg-mul-1 75.5%

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

   4. Simplified 75.5%

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

   if -3.19999999999999975e-64 < d < 1.9199999999999999e99

   1. Initial program 73.4%

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

   2. Taylor expanded in c around inf 65.2%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;d \leq -3.2 \cdot 10^{-64} \lor \neg \left(d \leq 1.92 \cdot 10^{+99}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \]

Alternative 9: 41.7% 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 60.0%

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

2. Taylor expanded in c around inf 39.3%

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

3. Final simplification 39.3%

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

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 2023257 
(FPCore (a b c d)
  :name "Complex division, imag part"
  :precision binary64

  :herbie-target
  (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))))