Complex division, imag part

Percentage Accurate: 62.0% → 85.4%

Time: 13.1s

Alternatives: 12

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: 62.0% 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: 85.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \leq 10^{+302}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{\mathsf{fma}\left(b, c, a \cdot \left(-d\right)\right)}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= (/ (- (* b c) (* a d)) (+ (* c c) (* d d))) 1e+302)
   (* (/ 1.0 (hypot c d)) (/ (fma b c (* a (- d))) (hypot c d)))
   (- (/ b c) (* (/ d c) (/ a c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((((b * c) - (a * d)) / ((c * c) + (d * d))) <= 1e+302) {
		tmp = (1.0 / hypot(c, d)) * (fma(b, c, (a * -d)) / hypot(c, d));
	} else {
		tmp = (b / c) - ((d / c) * (a / c));
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (Float64(Float64(Float64(b * c) - Float64(a * d)) / Float64(Float64(c * c) + Float64(d * d))) <= 1e+302)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * Float64(fma(b, c, Float64(a * Float64(-d))) / hypot(c, d)));
	else
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[N[(N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+302], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(N[(b * c + N[(a * (-d)), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 82.4% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -3.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \mathsf{fma}\left(-1, b, \frac{a}{\frac{c}{d}}\right)\\ \mathbf{elif}\;c \leq -3 \cdot 10^{-159}:\\ \;\;\;\;\mathsf{fma}\left(b, c, a \cdot \left(-d\right)\right) \cdot \frac{1}{{\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}}\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-162}:\\ \;\;\;\;\frac{b}{d \cdot \frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;c \leq 5.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -3.3e+103)
   (* (/ 1.0 (hypot c d)) (fma -1.0 b (/ a (/ c d))))
   (if (<= c -3e-159)
     (* (fma b c (* a (- d))) (/ 1.0 (pow (hypot c d) 2.0)))
     (if (<= c 2.4e-162)
       (- (/ b (* d (/ d c))) (/ a d))
       (if (<= c 5.4e+101)
         (/ (- (* b c) (* a d)) (+ (* c c) (* d d)))
         (- (/ b c) (* (/ d c) (/ a c))))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -3.3e+103) {
		tmp = (1.0 / hypot(c, d)) * fma(-1.0, b, (a / (c / d)));
	} else if (c <= -3e-159) {
		tmp = fma(b, c, (a * -d)) * (1.0 / pow(hypot(c, d), 2.0));
	} else if (c <= 2.4e-162) {
		tmp = (b / (d * (d / c))) - (a / d);
	} else if (c <= 5.4e+101) {
		tmp = ((b * c) - (a * d)) / ((c * c) + (d * d));
	} else {
		tmp = (b / c) - ((d / c) * (a / c));
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -3.3e+103)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * fma(-1.0, b, Float64(a / Float64(c / d))));
	elseif (c <= -3e-159)
		tmp = Float64(fma(b, c, Float64(a * Float64(-d))) * Float64(1.0 / (hypot(c, d) ^ 2.0)));
	elseif (c <= 2.4e-162)
		tmp = Float64(Float64(b / Float64(d * Float64(d / c))) - Float64(a / d));
	elseif (c <= 5.4e+101)
		tmp = Float64(Float64(Float64(b * c) - Float64(a * d)) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -3.3e+103], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(-1.0 * b + N[(a / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3e-159], N[(N[(b * c + N[(a * (-d)), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e-162], N[(N[(b / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.4e+101], N[(N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 82.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\\ \mathbf{if}\;c \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;\frac{1}{\mathsf{hypot}\left(c, d\right)} \cdot \mathsf{fma}\left(-1, b, \frac{a}{\frac{c}{d}}\right)\\ \mathbf{elif}\;c \leq -2.6 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 1.65 \cdot 10^{-162}:\\ \;\;\;\;\frac{b}{d \cdot \frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* b c) (* a d)) (+ (* c c) (* d d)))))
   (if (<= c -1.05e+103)
     (* (/ 1.0 (hypot c d)) (fma -1.0 b (/ a (/ c d))))
     (if (<= c -2.6e-134)
       t_0
       (if (<= c 1.65e-162)
         (- (/ b (* d (/ d c))) (/ a d))
         (if (<= c 4.8e+101) t_0 (- (/ b c) (* (/ d c) (/ a c)))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (a * d)) / ((c * c) + (d * d));
	double tmp;
	if (c <= -1.05e+103) {
		tmp = (1.0 / hypot(c, d)) * fma(-1.0, b, (a / (c / d)));
	} else if (c <= -2.6e-134) {
		tmp = t_0;
	} else if (c <= 1.65e-162) {
		tmp = (b / (d * (d / c))) - (a / d);
	} else if (c <= 4.8e+101) {
		tmp = t_0;
	} else {
		tmp = (b / c) - ((d / c) * (a / c));
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(b * c) - Float64(a * d)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (c <= -1.05e+103)
		tmp = Float64(Float64(1.0 / hypot(c, d)) * fma(-1.0, b, Float64(a / Float64(c / d))));
	elseif (c <= -2.6e-134)
		tmp = t_0;
	elseif (c <= 1.65e-162)
		tmp = Float64(Float64(b / Float64(d * Float64(d / c))) - Float64(a / d));
	elseif (c <= 4.8e+101)
		tmp = t_0;
	else
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)));
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.05e+103], N[(N[(1.0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(-1.0 * b + N[(a / N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -2.6e-134], t$95$0, If[LessEqual[c, 1.65e-162], N[(N[(b / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 4.8e+101], t$95$0, N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 82.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d}\\ t_1 := \frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \mathbf{if}\;c \leq -8.2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -2.8 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;c \leq 2.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{b}{d \cdot \frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;c \leq 5.3 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))
        (t_1 (- (/ b c) (* (/ d c) (/ a c)))))
   (if (<= c -8.2e+103)
     t_1
     (if (<= c -2.8e-131)
       t_0
       (if (<= c 2.6e-162)
         (- (/ b (* d (/ d c))) (/ a d))
         (if (<= c 5.3e+101) t_0 t_1))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (a * d)) / ((c * c) + (d * d));
	double t_1 = (b / c) - ((d / c) * (a / c));
	double tmp;
	if (c <= -8.2e+103) {
		tmp = t_1;
	} else if (c <= -2.8e-131) {
		tmp = t_0;
	} else if (c <= 2.6e-162) {
		tmp = (b / (d * (d / c))) - (a / d);
	} else if (c <= 5.3e+101) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((b * c) - (a * d)) / ((c * c) + (d * d))
    t_1 = (b / c) - ((d / c) * (a / c))
    if (c <= (-8.2d+103)) then
        tmp = t_1
    else if (c <= (-2.8d-131)) then
        tmp = t_0
    else if (c <= 2.6d-162) then
        tmp = (b / (d * (d / c))) - (a / d)
    else if (c <= 5.3d+101) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (a * d)) / ((c * c) + (d * d));
	double t_1 = (b / c) - ((d / c) * (a / c));
	double tmp;
	if (c <= -8.2e+103) {
		tmp = t_1;
	} else if (c <= -2.8e-131) {
		tmp = t_0;
	} else if (c <= 2.6e-162) {
		tmp = (b / (d * (d / c))) - (a / d);
	} else if (c <= 5.3e+101) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((b * c) - (a * d)) / ((c * c) + (d * d))
	t_1 = (b / c) - ((d / c) * (a / c))
	tmp = 0
	if c <= -8.2e+103:
		tmp = t_1
	elif c <= -2.8e-131:
		tmp = t_0
	elif c <= 2.6e-162:
		tmp = (b / (d * (d / c))) - (a / d)
	elif c <= 5.3e+101:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(b * c) - Float64(a * d)) / Float64(Float64(c * c) + Float64(d * d)))
	t_1 = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)))
	tmp = 0.0
	if (c <= -8.2e+103)
		tmp = t_1;
	elseif (c <= -2.8e-131)
		tmp = t_0;
	elseif (c <= 2.6e-162)
		tmp = Float64(Float64(b / Float64(d * Float64(d / c))) - Float64(a / d));
	elseif (c <= 5.3e+101)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((b * c) - (a * d)) / ((c * c) + (d * d));
	t_1 = (b / c) - ((d / c) * (a / c));
	tmp = 0.0;
	if (c <= -8.2e+103)
		tmp = t_1;
	elseif (c <= -2.8e-131)
		tmp = t_0;
	elseif (c <= 2.6e-162)
		tmp = (b / (d * (d / c))) - (a / d);
	elseif (c <= 5.3e+101)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -8.2e+103], t$95$1, If[LessEqual[c, -2.8e-131], t$95$0, If[LessEqual[c, 2.6e-162], N[(N[(b / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 5.3e+101], t$95$0, t$95$1]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 71.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -0.00375 \lor \neg \left(d \leq 3.5 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -0.00375) (not (<= d 3.5e+67)))
   (/ (- a) d)
   (- (/ b c) (* (/ d c) (/ a c)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -0.00375) || !(d <= 3.5e+67)) {
		tmp = -a / d;
	} else {
		tmp = (b / c) - ((d / c) * (a / c));
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-0.00375d0)) .or. (.not. (d <= 3.5d+67))) then
        tmp = -a / d
    else
        tmp = (b / c) - ((d / c) * (a / c))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -0.00375) || !(d <= 3.5e+67)) {
		tmp = -a / d;
	} else {
		tmp = (b / c) - ((d / c) * (a / c));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -0.00375) or not (d <= 3.5e+67):
		tmp = -a / d
	else:
		tmp = (b / c) - ((d / c) * (a / c))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -0.00375) || !(d <= 3.5e+67))
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -0.00375) || ~((d <= 3.5e+67)))
		tmp = -a / d;
	else
		tmp = (b / c) - ((d / c) * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -0.00375], N[Not[LessEqual[d, 3.5e+67]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 71.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -0.0025 \lor \neg \left(d \leq 3.2 \cdot 10^{+67}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{d \cdot \frac{a}{c}}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -0.0025) (not (<= d 3.2e+67)))
   (/ (- a) d)
   (- (/ b c) (/ (* d (/ a c)) c))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -0.0025) || !(d <= 3.2e+67)) {
		tmp = -a / d;
	} else {
		tmp = (b / c) - ((d * (a / 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 <= (-0.0025d0)) .or. (.not. (d <= 3.2d+67))) then
        tmp = -a / d
    else
        tmp = (b / c) - ((d * (a / 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 <= -0.0025) || !(d <= 3.2e+67)) {
		tmp = -a / d;
	} else {
		tmp = (b / c) - ((d * (a / c)) / c);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -0.0025) or not (d <= 3.2e+67):
		tmp = -a / d
	else:
		tmp = (b / c) - ((d * (a / c)) / c)
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -0.0025) || !(d <= 3.2e+67))
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(Float64(b / c) - Float64(Float64(d * Float64(a / c)) / c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -0.0025) || ~((d <= 3.2e+67)))
		tmp = -a / d;
	else
		tmp = (b / c) - ((d * (a / c)) / c);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -0.0025], N[Not[LessEqual[d, 3.2e+67]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(N[(b / c), $MachinePrecision] - N[(N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 74.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -6.3 \cdot 10^{-6}:\\ \;\;\;\;\frac{b}{c} - \frac{d \cdot \frac{a}{c}}{c}\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{b}{\frac{d \cdot d}{c}} - \frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -6.3e-6)
   (- (/ b c) (/ (* d (/ a c)) c))
   (if (<= c 2.4e-34)
     (- (/ b (/ (* d d) c)) (/ a d))
     (- (/ b c) (* (/ d c) (/ a c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -6.3e-6) {
		tmp = (b / c) - ((d * (a / c)) / c);
	} else if (c <= 2.4e-34) {
		tmp = (b / ((d * d) / c)) - (a / d);
	} else {
		tmp = (b / c) - ((d / c) * (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 <= (-6.3d-6)) then
        tmp = (b / c) - ((d * (a / c)) / c)
    else if (c <= 2.4d-34) then
        tmp = (b / ((d * d) / c)) - (a / d)
    else
        tmp = (b / c) - ((d / c) * (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 <= -6.3e-6) {
		tmp = (b / c) - ((d * (a / c)) / c);
	} else if (c <= 2.4e-34) {
		tmp = (b / ((d * d) / c)) - (a / d);
	} else {
		tmp = (b / c) - ((d / c) * (a / c));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -6.3e-6:
		tmp = (b / c) - ((d * (a / c)) / c)
	elif c <= 2.4e-34:
		tmp = (b / ((d * d) / c)) - (a / d)
	else:
		tmp = (b / c) - ((d / c) * (a / c))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -6.3e-6)
		tmp = Float64(Float64(b / c) - Float64(Float64(d * Float64(a / c)) / c));
	elseif (c <= 2.4e-34)
		tmp = Float64(Float64(b / Float64(Float64(d * d) / c)) - Float64(a / d));
	else
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -6.3e-6)
		tmp = (b / c) - ((d * (a / c)) / c);
	elseif (c <= 2.4e-34)
		tmp = (b / ((d * d) / c)) - (a / d);
	else
		tmp = (b / c) - ((d / c) * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -6.3e-6], N[(N[(b / c), $MachinePrecision] - N[(N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.4e-34], N[(N[(b / N[(N[(d * d), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -0.000206:\\ \;\;\;\;\frac{b}{c} - \frac{d \cdot \frac{a}{c}}{c}\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-35}:\\ \;\;\;\;\frac{b}{d \cdot \frac{d}{c}} - \frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - \frac{d}{c} \cdot \frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -0.000206)
   (- (/ b c) (/ (* d (/ a c)) c))
   (if (<= c 2.1e-35)
     (- (/ b (* d (/ d c))) (/ a d))
     (- (/ b c) (* (/ d c) (/ a c))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -0.000206) {
		tmp = (b / c) - ((d * (a / c)) / c);
	} else if (c <= 2.1e-35) {
		tmp = (b / (d * (d / c))) - (a / d);
	} else {
		tmp = (b / c) - ((d / c) * (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 <= (-0.000206d0)) then
        tmp = (b / c) - ((d * (a / c)) / c)
    else if (c <= 2.1d-35) then
        tmp = (b / (d * (d / c))) - (a / d)
    else
        tmp = (b / c) - ((d / c) * (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 <= -0.000206) {
		tmp = (b / c) - ((d * (a / c)) / c);
	} else if (c <= 2.1e-35) {
		tmp = (b / (d * (d / c))) - (a / d);
	} else {
		tmp = (b / c) - ((d / c) * (a / c));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -0.000206:
		tmp = (b / c) - ((d * (a / c)) / c)
	elif c <= 2.1e-35:
		tmp = (b / (d * (d / c))) - (a / d)
	else:
		tmp = (b / c) - ((d / c) * (a / c))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -0.000206)
		tmp = Float64(Float64(b / c) - Float64(Float64(d * Float64(a / c)) / c));
	elseif (c <= 2.1e-35)
		tmp = Float64(Float64(b / Float64(d * Float64(d / c))) - Float64(a / d));
	else
		tmp = Float64(Float64(b / c) - Float64(Float64(d / c) * Float64(a / c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -0.000206)
		tmp = (b / c) - ((d * (a / c)) / c);
	elseif (c <= 2.1e-35)
		tmp = (b / (d * (d / c))) - (a / d);
	else
		tmp = (b / c) - ((d / c) * (a / c));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -0.000206], N[(N[(b / c), $MachinePrecision] - N[(N[(d * N[(a / c), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.1e-35], N[(N[(b / N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] - N[(N[(d / c), $MachinePrecision] * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 62.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -2.7 \cdot 10^{-59} \lor \neg \left(d \leq 8.5 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -2.7e-59) (not (<= d 8.5e+63))) (/ (- a) d) (/ b c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -2.7e-59) || !(d <= 8.5e+63)) {
		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 <= (-2.7d-59)) .or. (.not. (d <= 8.5d+63))) 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 <= -2.7e-59) || !(d <= 8.5e+63)) {
		tmp = -a / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -2.7e-59) or not (d <= 8.5e+63):
		tmp = -a / d
	else:
		tmp = b / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -2.7e-59) || !(d <= 8.5e+63))
		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 <= -2.7e-59) || ~((d <= 8.5e+63)))
		tmp = -a / d;
	else
		tmp = b / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -2.7e-59], N[Not[LessEqual[d, 8.5e+63]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(b / c), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 14.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -8.6 \cdot 10^{+76} \lor \neg \left(d \leq 2.2 \cdot 10^{+156}\right):\\ \;\;\;\;\frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -8.6e+76) (not (<= d 2.2e+156))) (/ a d) (/ a c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -8.6e+76) || !(d <= 2.2e+156)) {
		tmp = a / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-8.6d+76)) .or. (.not. (d <= 2.2d+156))) then
        tmp = a / d
    else
        tmp = a / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -8.6e+76) || !(d <= 2.2e+156)) {
		tmp = a / d;
	} else {
		tmp = a / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -8.6e+76) or not (d <= 2.2e+156):
		tmp = a / d
	else:
		tmp = a / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -8.6e+76) || !(d <= 2.2e+156))
		tmp = Float64(a / d);
	else
		tmp = Float64(a / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -8.6e+76) || ~((d <= 2.2e+156)))
		tmp = a / d;
	else
		tmp = a / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -8.6e+76], N[Not[LessEqual[d, 2.2e+156]], $MachinePrecision]], N[(a / d), $MachinePrecision], N[(a / c), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 45.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.35 \cdot 10^{+119} \lor \neg \left(d \leq 1.45 \cdot 10^{+195}\right):\\ \;\;\;\;\frac{a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.35e+119) (not (<= d 1.45e+195))) (/ a d) (/ b c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.35e+119) || !(d <= 1.45e+195)) {
		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 <= (-1.35d+119)) .or. (.not. (d <= 1.45d+195))) 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 <= -1.35e+119) || !(d <= 1.45e+195)) {
		tmp = a / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.35e+119) or not (d <= 1.45e+195):
		tmp = a / d
	else:
		tmp = b / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.35e+119) || !(d <= 1.45e+195))
		tmp = 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 <= -1.35e+119) || ~((d <= 1.45e+195)))
		tmp = a / d;
	else
		tmp = b / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -1.35e+119], N[Not[LessEqual[d, 1.45e+195]], $MachinePrecision]], N[(a / d), $MachinePrecision], N[(b / c), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 9.8% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.4% 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 2024006 
(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))))