Complex division, imag part

Percentage Accurate: 61.9% → 77.0%

Time: 11.8s

Alternatives: 15

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: 61.9% 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: 77.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -1.65 \cdot 10^{+92}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -2.5 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{a}{c \cdot \left(c \cdot \frac{1}{d}\right)}, \frac{b}{c}\right)\\ \mathbf{elif}\;d \leq -6 \cdot 10^{+56}:\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{elif}\;d \leq -0.003:\\ \;\;\;\;\frac{b}{c} - d \cdot \frac{a}{{c}^{2}}\\ \mathbf{elif}\;d \leq -7.8 \cdot 10^{-137}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\frac{a}{c}}{\frac{c}{d}}, \frac{b}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ (* c (/ b d)) d) (/ a d))))
   (if (<= d -1.65e+92)
     t_0
     (if (<= d -2.5e+77)
       (fma -1.0 (/ a (* c (* c (/ 1.0 d)))) (/ b c))
       (if (<= d -6e+56)
         (/ (- a) d)
         (if (<= d -0.003)
           (- (/ b c) (* d (/ a (pow c 2.0))))
           (if (<= d -7.8e-137)
             (/ (- (* c b) (* d a)) (+ (* c c) (* d d)))
             (if (<= d 2.55e+36)
               (fma -1.0 (/ (/ a c) (/ c d)) (/ b c))
               t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -1.65e+92) {
		tmp = t_0;
	} else if (d <= -2.5e+77) {
		tmp = fma(-1.0, (a / (c * (c * (1.0 / d)))), (b / c));
	} else if (d <= -6e+56) {
		tmp = -a / d;
	} else if (d <= -0.003) {
		tmp = (b / c) - (d * (a / pow(c, 2.0)));
	} else if (d <= -7.8e-137) {
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	} else if (d <= 2.55e+36) {
		tmp = fma(-1.0, ((a / c) / (c / d)), (b / c));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d))
	tmp = 0.0
	if (d <= -1.65e+92)
		tmp = t_0;
	elseif (d <= -2.5e+77)
		tmp = fma(-1.0, Float64(a / Float64(c * Float64(c * Float64(1.0 / d)))), Float64(b / c));
	elseif (d <= -6e+56)
		tmp = Float64(Float64(-a) / d);
	elseif (d <= -0.003)
		tmp = Float64(Float64(b / c) - Float64(d * Float64(a / (c ^ 2.0))));
	elseif (d <= -7.8e-137)
		tmp = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 2.55e+36)
		tmp = fma(-1.0, Float64(Float64(a / c) / Float64(c / d)), Float64(b / c));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.65e+92], t$95$0, If[LessEqual[d, -2.5e+77], N[(-1.0 * N[(a / N[(c * N[(c * N[(1.0 / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -6e+56], N[((-a) / d), $MachinePrecision], If[LessEqual[d, -0.003], N[(N[(b / c), $MachinePrecision] - N[(d * N[(a / N[Power[c, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -7.8e-137], N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2.55e+36], N[(-1.0 * N[(N[(a / c), $MachinePrecision] / N[(c / d), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 2: 77.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(-1, \frac{a}{c \cdot \frac{c}{d}}, \frac{b}{c}\right)\\ t_1 := \frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -5.4 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -2.2 \cdot 10^{+77}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -1.05 \cdot 10^{+57}:\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{elif}\;d \leq -0.06:\\ \;\;\;\;\frac{b}{c} - d \cdot \frac{a}{{c}^{2}}\\ \mathbf{elif}\;d \leq -3.35 \cdot 10^{-137}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 8.5 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (fma -1.0 (/ a (* c (/ c d))) (/ b c)))
        (t_1 (- (/ (* c (/ b d)) d) (/ a d))))
   (if (<= d -5.4e+85)
     t_1
     (if (<= d -2.2e+77)
       t_0
       (if (<= d -1.05e+57)
         (/ (- a) d)
         (if (<= d -0.06)
           (- (/ b c) (* d (/ a (pow c 2.0))))
           (if (<= d -3.35e-137)
             (/ (- (* c b) (* d a)) (+ (* c c) (* d d)))
             (if (<= d 8.5e+30) t_0 t_1))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = fma(-1.0, (a / (c * (c / d))), (b / c));
	double t_1 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -5.4e+85) {
		tmp = t_1;
	} else if (d <= -2.2e+77) {
		tmp = t_0;
	} else if (d <= -1.05e+57) {
		tmp = -a / d;
	} else if (d <= -0.06) {
		tmp = (b / c) - (d * (a / pow(c, 2.0)));
	} else if (d <= -3.35e-137) {
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	} else if (d <= 8.5e+30) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = fma(-1.0, Float64(a / Float64(c * Float64(c / d))), Float64(b / c))
	t_1 = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d))
	tmp = 0.0
	if (d <= -5.4e+85)
		tmp = t_1;
	elseif (d <= -2.2e+77)
		tmp = t_0;
	elseif (d <= -1.05e+57)
		tmp = Float64(Float64(-a) / d);
	elseif (d <= -0.06)
		tmp = Float64(Float64(b / c) - Float64(d * Float64(a / (c ^ 2.0))));
	elseif (d <= -3.35e-137)
		tmp = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 8.5e+30)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(-1.0 * N[(a / N[(c * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -5.4e+85], t$95$1, If[LessEqual[d, -2.2e+77], t$95$0, If[LessEqual[d, -1.05e+57], N[((-a) / d), $MachinePrecision], If[LessEqual[d, -0.06], N[(N[(b / c), $MachinePrecision] - N[(d * N[(a / N[Power[c, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -3.35e-137], N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 8.5e+30], t$95$0, t$95$1]]]]]]]]

Derivation

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

Alternative 3: 77.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -5.3 \cdot 10^{+85}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -3.1 \cdot 10^{+76}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{a}{c \cdot \frac{c}{d}}, \frac{b}{c}\right)\\ \mathbf{elif}\;d \leq -2.25 \cdot 10^{+55}:\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{elif}\;d \leq -0.0048:\\ \;\;\;\;\frac{b}{c} - d \cdot \frac{a}{{c}^{2}}\\ \mathbf{elif}\;d \leq -2.85 \cdot 10^{-139}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 8.2 \cdot 10^{+38}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{\frac{a}{c}}{\frac{c}{d}}, \frac{b}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ (* c (/ b d)) d) (/ a d))))
   (if (<= d -5.3e+85)
     t_0
     (if (<= d -3.1e+76)
       (fma -1.0 (/ a (* c (/ c d))) (/ b c))
       (if (<= d -2.25e+55)
         (/ (- a) d)
         (if (<= d -0.0048)
           (- (/ b c) (* d (/ a (pow c 2.0))))
           (if (<= d -2.85e-139)
             (/ (- (* c b) (* d a)) (+ (* c c) (* d d)))
             (if (<= d 8.2e+38)
               (fma -1.0 (/ (/ a c) (/ c d)) (/ b c))
               t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -5.3e+85) {
		tmp = t_0;
	} else if (d <= -3.1e+76) {
		tmp = fma(-1.0, (a / (c * (c / d))), (b / c));
	} else if (d <= -2.25e+55) {
		tmp = -a / d;
	} else if (d <= -0.0048) {
		tmp = (b / c) - (d * (a / pow(c, 2.0)));
	} else if (d <= -2.85e-139) {
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	} else if (d <= 8.2e+38) {
		tmp = fma(-1.0, ((a / c) / (c / d)), (b / c));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d))
	tmp = 0.0
	if (d <= -5.3e+85)
		tmp = t_0;
	elseif (d <= -3.1e+76)
		tmp = fma(-1.0, Float64(a / Float64(c * Float64(c / d))), Float64(b / c));
	elseif (d <= -2.25e+55)
		tmp = Float64(Float64(-a) / d);
	elseif (d <= -0.0048)
		tmp = Float64(Float64(b / c) - Float64(d * Float64(a / (c ^ 2.0))));
	elseif (d <= -2.85e-139)
		tmp = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 8.2e+38)
		tmp = fma(-1.0, Float64(Float64(a / c) / Float64(c / d)), Float64(b / c));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -5.3e+85], t$95$0, If[LessEqual[d, -3.1e+76], N[(-1.0 * N[(a / N[(c * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -2.25e+55], N[((-a) / d), $MachinePrecision], If[LessEqual[d, -0.0048], N[(N[(b / c), $MachinePrecision] - N[(d * N[(a / N[Power[c, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -2.85e-139], N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 8.2e+38], N[(-1.0 * N[(N[(a / c), $MachinePrecision] / N[(c / d), $MachinePrecision]), $MachinePrecision] + N[(b / c), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 4: 75.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b}{c} - d \cdot \frac{a}{{c}^{2}}\\ t_1 := \frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -1.36 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;d \leq -0.2:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -2.7 \cdot 10^{-137}:\\ \;\;\;\;\frac{c \cdot b - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 6.2 \cdot 10^{+31}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ b c) (* d (/ a (pow c 2.0)))))
        (t_1 (- (/ (* c (/ b d)) d) (/ a d))))
   (if (<= d -1.36e+54)
     t_1
     (if (<= d -0.2)
       t_0
       (if (<= d -2.7e-137)
         (/ (- (* c b) (* d a)) (+ (* c c) (* d d)))
         (if (<= d 6.2e+31) t_0 t_1))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b / c) - (d * (a / pow(c, 2.0)));
	double t_1 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -1.36e+54) {
		tmp = t_1;
	} else if (d <= -0.2) {
		tmp = t_0;
	} else if (d <= -2.7e-137) {
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	} else if (d <= 6.2e+31) {
		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) - (d * (a / (c ** 2.0d0)))
    t_1 = ((c * (b / d)) / d) - (a / d)
    if (d <= (-1.36d+54)) then
        tmp = t_1
    else if (d <= (-0.2d0)) then
        tmp = t_0
    else if (d <= (-2.7d-137)) then
        tmp = ((c * b) - (d * a)) / ((c * c) + (d * d))
    else if (d <= 6.2d+31) 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) - (d * (a / Math.pow(c, 2.0)));
	double t_1 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -1.36e+54) {
		tmp = t_1;
	} else if (d <= -0.2) {
		tmp = t_0;
	} else if (d <= -2.7e-137) {
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	} else if (d <= 6.2e+31) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b / c) - (d * (a / math.pow(c, 2.0)))
	t_1 = ((c * (b / d)) / d) - (a / d)
	tmp = 0
	if d <= -1.36e+54:
		tmp = t_1
	elif d <= -0.2:
		tmp = t_0
	elif d <= -2.7e-137:
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d))
	elif d <= 6.2e+31:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b / c) - Float64(d * Float64(a / (c ^ 2.0))))
	t_1 = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d))
	tmp = 0.0
	if (d <= -1.36e+54)
		tmp = t_1;
	elseif (d <= -0.2)
		tmp = t_0;
	elseif (d <= -2.7e-137)
		tmp = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 6.2e+31)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b / c) - (d * (a / (c ^ 2.0)));
	t_1 = ((c * (b / d)) / d) - (a / d);
	tmp = 0.0;
	if (d <= -1.36e+54)
		tmp = t_1;
	elseif (d <= -0.2)
		tmp = t_0;
	elseif (d <= -2.7e-137)
		tmp = ((c * b) - (d * a)) / ((c * c) + (d * d));
	elseif (d <= 6.2e+31)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b / c), $MachinePrecision] - N[(d * N[(a / N[Power[c, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.36e+54], t$95$1, If[LessEqual[d, -0.2], t$95$0, If[LessEqual[d, -2.7e-137], N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 6.2e+31], t$95$0, t$95$1]]]]]]

Derivation

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

Alternative 5: 66.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := c \cdot \frac{\frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -1.2 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -9.2 \cdot 10^{-12}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq -5.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{elif}\;d \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{a}{c}}{\frac{-c}{d}}\\ \mathbf{elif}\;d \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (* c (/ (/ b d) d)) (/ a d))))
   (if (<= d -1.2e+54)
     t_0
     (if (<= d -9.2e-12)
       (/ b c)
       (if (<= d -5.2e-72)
         (/ (- a) d)
         (if (<= d 4.8e-217)
           (/ b c)
           (if (<= d 1.9e-184)
             (/ (/ a c) (/ (- c) d))
             (if (<= d 9.2e+29) (/ b c) t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (c * ((b / d) / d)) - (a / d);
	double tmp;
	if (d <= -1.2e+54) {
		tmp = t_0;
	} else if (d <= -9.2e-12) {
		tmp = b / c;
	} else if (d <= -5.2e-72) {
		tmp = -a / d;
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 9.2e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (c * ((b / d) / d)) - (a / d)
    if (d <= (-1.2d+54)) then
        tmp = t_0
    else if (d <= (-9.2d-12)) then
        tmp = b / c
    else if (d <= (-5.2d-72)) then
        tmp = -a / d
    else if (d <= 4.8d-217) then
        tmp = b / c
    else if (d <= 1.9d-184) then
        tmp = (a / c) / (-c / d)
    else if (d <= 9.2d+29) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (c * ((b / d) / d)) - (a / d);
	double tmp;
	if (d <= -1.2e+54) {
		tmp = t_0;
	} else if (d <= -9.2e-12) {
		tmp = b / c;
	} else if (d <= -5.2e-72) {
		tmp = -a / d;
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 9.2e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (c * ((b / d) / d)) - (a / d)
	tmp = 0
	if d <= -1.2e+54:
		tmp = t_0
	elif d <= -9.2e-12:
		tmp = b / c
	elif d <= -5.2e-72:
		tmp = -a / d
	elif d <= 4.8e-217:
		tmp = b / c
	elif d <= 1.9e-184:
		tmp = (a / c) / (-c / d)
	elif d <= 9.2e+29:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(c * Float64(Float64(b / d) / d)) - Float64(a / d))
	tmp = 0.0
	if (d <= -1.2e+54)
		tmp = t_0;
	elseif (d <= -9.2e-12)
		tmp = Float64(b / c);
	elseif (d <= -5.2e-72)
		tmp = Float64(Float64(-a) / d);
	elseif (d <= 4.8e-217)
		tmp = Float64(b / c);
	elseif (d <= 1.9e-184)
		tmp = Float64(Float64(a / c) / Float64(Float64(-c) / d));
	elseif (d <= 9.2e+29)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (c * ((b / d) / d)) - (a / d);
	tmp = 0.0;
	if (d <= -1.2e+54)
		tmp = t_0;
	elseif (d <= -9.2e-12)
		tmp = b / c;
	elseif (d <= -5.2e-72)
		tmp = -a / d;
	elseif (d <= 4.8e-217)
		tmp = b / c;
	elseif (d <= 1.9e-184)
		tmp = (a / c) / (-c / d);
	elseif (d <= 9.2e+29)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(c * N[(N[(b / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.2e+54], t$95$0, If[LessEqual[d, -9.2e-12], N[(b / c), $MachinePrecision], If[LessEqual[d, -5.2e-72], N[((-a) / d), $MachinePrecision], If[LessEqual[d, 4.8e-217], N[(b / c), $MachinePrecision], If[LessEqual[d, 1.9e-184], N[(N[(a / c), $MachinePrecision] / N[((-c) / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 9.2e+29], N[(b / c), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 6: 67.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -7.5 \cdot 10^{+53}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -3.3 \cdot 10^{-9}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq -6.8 \cdot 10^{-71}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{a}{c}}{\frac{-c}{d}}\\ \mathbf{elif}\;d \leq 5.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ (* c (/ b d)) d) (/ a d))))
   (if (<= d -7.5e+53)
     t_0
     (if (<= d -3.3e-9)
       (/ b c)
       (if (<= d -6.8e-71)
         t_0
         (if (<= d 4.8e-217)
           (/ b c)
           (if (<= d 1.9e-184)
             (/ (/ a c) (/ (- c) d))
             (if (<= d 5.5e+29) (/ b c) t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -7.5e+53) {
		tmp = t_0;
	} else if (d <= -3.3e-9) {
		tmp = b / c;
	} else if (d <= -6.8e-71) {
		tmp = t_0;
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 5.5e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((c * (b / d)) / d) - (a / d)
    if (d <= (-7.5d+53)) then
        tmp = t_0
    else if (d <= (-3.3d-9)) then
        tmp = b / c
    else if (d <= (-6.8d-71)) then
        tmp = t_0
    else if (d <= 4.8d-217) then
        tmp = b / c
    else if (d <= 1.9d-184) then
        tmp = (a / c) / (-c / d)
    else if (d <= 5.5d+29) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -7.5e+53) {
		tmp = t_0;
	} else if (d <= -3.3e-9) {
		tmp = b / c;
	} else if (d <= -6.8e-71) {
		tmp = t_0;
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 5.5e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * (b / d)) / d) - (a / d)
	tmp = 0
	if d <= -7.5e+53:
		tmp = t_0
	elif d <= -3.3e-9:
		tmp = b / c
	elif d <= -6.8e-71:
		tmp = t_0
	elif d <= 4.8e-217:
		tmp = b / c
	elif d <= 1.9e-184:
		tmp = (a / c) / (-c / d)
	elif d <= 5.5e+29:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d))
	tmp = 0.0
	if (d <= -7.5e+53)
		tmp = t_0;
	elseif (d <= -3.3e-9)
		tmp = Float64(b / c);
	elseif (d <= -6.8e-71)
		tmp = t_0;
	elseif (d <= 4.8e-217)
		tmp = Float64(b / c);
	elseif (d <= 1.9e-184)
		tmp = Float64(Float64(a / c) / Float64(Float64(-c) / d));
	elseif (d <= 5.5e+29)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * (b / d)) / d) - (a / d);
	tmp = 0.0;
	if (d <= -7.5e+53)
		tmp = t_0;
	elseif (d <= -3.3e-9)
		tmp = b / c;
	elseif (d <= -6.8e-71)
		tmp = t_0;
	elseif (d <= 4.8e-217)
		tmp = b / c;
	elseif (d <= 1.9e-184)
		tmp = (a / c) / (-c / d);
	elseif (d <= 5.5e+29)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -7.5e+53], t$95$0, If[LessEqual[d, -3.3e-9], N[(b / c), $MachinePrecision], If[LessEqual[d, -6.8e-71], t$95$0, If[LessEqual[d, 4.8e-217], N[(b / c), $MachinePrecision], If[LessEqual[d, 1.9e-184], N[(N[(a / c), $MachinePrecision] / N[((-c) / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 5.5e+29], N[(b / c), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 7: 67.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -1.2 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -6.8 \cdot 10^{-13}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq -1 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{c}{d}}{\frac{d}{b}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{a}{c}}{\frac{-c}{d}}\\ \mathbf{elif}\;d \leq 5.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ (* c (/ b d)) d) (/ a d))))
   (if (<= d -1.2e+54)
     t_0
     (if (<= d -6.8e-13)
       (/ b c)
       (if (<= d -1e-70)
         (- (/ (/ c d) (/ d b)) (/ a d))
         (if (<= d 4.8e-217)
           (/ b c)
           (if (<= d 1.9e-184)
             (/ (/ a c) (/ (- c) d))
             (if (<= d 5.5e+29) (/ b c) t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -1.2e+54) {
		tmp = t_0;
	} else if (d <= -6.8e-13) {
		tmp = b / c;
	} else if (d <= -1e-70) {
		tmp = ((c / d) / (d / b)) - (a / d);
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 5.5e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((c * (b / d)) / d) - (a / d)
    if (d <= (-1.2d+54)) then
        tmp = t_0
    else if (d <= (-6.8d-13)) then
        tmp = b / c
    else if (d <= (-1d-70)) then
        tmp = ((c / d) / (d / b)) - (a / d)
    else if (d <= 4.8d-217) then
        tmp = b / c
    else if (d <= 1.9d-184) then
        tmp = (a / c) / (-c / d)
    else if (d <= 5.5d+29) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -1.2e+54) {
		tmp = t_0;
	} else if (d <= -6.8e-13) {
		tmp = b / c;
	} else if (d <= -1e-70) {
		tmp = ((c / d) / (d / b)) - (a / d);
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 5.5e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * (b / d)) / d) - (a / d)
	tmp = 0
	if d <= -1.2e+54:
		tmp = t_0
	elif d <= -6.8e-13:
		tmp = b / c
	elif d <= -1e-70:
		tmp = ((c / d) / (d / b)) - (a / d)
	elif d <= 4.8e-217:
		tmp = b / c
	elif d <= 1.9e-184:
		tmp = (a / c) / (-c / d)
	elif d <= 5.5e+29:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d))
	tmp = 0.0
	if (d <= -1.2e+54)
		tmp = t_0;
	elseif (d <= -6.8e-13)
		tmp = Float64(b / c);
	elseif (d <= -1e-70)
		tmp = Float64(Float64(Float64(c / d) / Float64(d / b)) - Float64(a / d));
	elseif (d <= 4.8e-217)
		tmp = Float64(b / c);
	elseif (d <= 1.9e-184)
		tmp = Float64(Float64(a / c) / Float64(Float64(-c) / d));
	elseif (d <= 5.5e+29)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * (b / d)) / d) - (a / d);
	tmp = 0.0;
	if (d <= -1.2e+54)
		tmp = t_0;
	elseif (d <= -6.8e-13)
		tmp = b / c;
	elseif (d <= -1e-70)
		tmp = ((c / d) / (d / b)) - (a / d);
	elseif (d <= 4.8e-217)
		tmp = b / c;
	elseif (d <= 1.9e-184)
		tmp = (a / c) / (-c / d);
	elseif (d <= 5.5e+29)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.2e+54], t$95$0, If[LessEqual[d, -6.8e-13], N[(b / c), $MachinePrecision], If[LessEqual[d, -1e-70], N[(N[(N[(c / d), $MachinePrecision] / N[(d / b), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 4.8e-217], N[(b / c), $MachinePrecision], If[LessEqual[d, 1.9e-184], N[(N[(a / c), $MachinePrecision] / N[((-c) / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 5.5e+29], N[(b / c), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 8: 67.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{if}\;d \leq -1.2 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -2 \cdot 10^{-12}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq -1.65 \cdot 10^{-71}:\\ \;\;\;\;\frac{\frac{c \cdot b}{d}}{d} - \frac{a}{d}\\ \mathbf{elif}\;d \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{a}{c}}{\frac{-c}{d}}\\ \mathbf{elif}\;d \leq 5.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ (* c (/ b d)) d) (/ a d))))
   (if (<= d -1.2e+54)
     t_0
     (if (<= d -2e-12)
       (/ b c)
       (if (<= d -1.65e-71)
         (- (/ (/ (* c b) d) d) (/ a d))
         (if (<= d 4.8e-217)
           (/ b c)
           (if (<= d 1.9e-184)
             (/ (/ a c) (/ (- c) d))
             (if (<= d 5.5e+29) (/ b c) t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -1.2e+54) {
		tmp = t_0;
	} else if (d <= -2e-12) {
		tmp = b / c;
	} else if (d <= -1.65e-71) {
		tmp = (((c * b) / d) / d) - (a / d);
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 5.5e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((c * (b / d)) / d) - (a / d)
    if (d <= (-1.2d+54)) then
        tmp = t_0
    else if (d <= (-2d-12)) then
        tmp = b / c
    else if (d <= (-1.65d-71)) then
        tmp = (((c * b) / d) / d) - (a / d)
    else if (d <= 4.8d-217) then
        tmp = b / c
    else if (d <= 1.9d-184) then
        tmp = (a / c) / (-c / d)
    else if (d <= 5.5d+29) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * (b / d)) / d) - (a / d);
	double tmp;
	if (d <= -1.2e+54) {
		tmp = t_0;
	} else if (d <= -2e-12) {
		tmp = b / c;
	} else if (d <= -1.65e-71) {
		tmp = (((c * b) / d) / d) - (a / d);
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 5.5e+29) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * (b / d)) / d) - (a / d)
	tmp = 0
	if d <= -1.2e+54:
		tmp = t_0
	elif d <= -2e-12:
		tmp = b / c
	elif d <= -1.65e-71:
		tmp = (((c * b) / d) / d) - (a / d)
	elif d <= 4.8e-217:
		tmp = b / c
	elif d <= 1.9e-184:
		tmp = (a / c) / (-c / d)
	elif d <= 5.5e+29:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d))
	tmp = 0.0
	if (d <= -1.2e+54)
		tmp = t_0;
	elseif (d <= -2e-12)
		tmp = Float64(b / c);
	elseif (d <= -1.65e-71)
		tmp = Float64(Float64(Float64(Float64(c * b) / d) / d) - Float64(a / d));
	elseif (d <= 4.8e-217)
		tmp = Float64(b / c);
	elseif (d <= 1.9e-184)
		tmp = Float64(Float64(a / c) / Float64(Float64(-c) / d));
	elseif (d <= 5.5e+29)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * (b / d)) / d) - (a / d);
	tmp = 0.0;
	if (d <= -1.2e+54)
		tmp = t_0;
	elseif (d <= -2e-12)
		tmp = b / c;
	elseif (d <= -1.65e-71)
		tmp = (((c * b) / d) / d) - (a / d);
	elseif (d <= 4.8e-217)
		tmp = b / c;
	elseif (d <= 1.9e-184)
		tmp = (a / c) / (-c / d);
	elseif (d <= 5.5e+29)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.2e+54], t$95$0, If[LessEqual[d, -2e-12], N[(b / c), $MachinePrecision], If[LessEqual[d, -1.65e-71], N[(N[(N[(N[(c * b), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 4.8e-217], N[(b / c), $MachinePrecision], If[LessEqual[d, 1.9e-184], N[(N[(a / c), $MachinePrecision] / N[((-c) / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 5.5e+29], N[(b / c), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 9: 78.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{c \cdot b - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{if}\;d \leq -2.2 \cdot 10^{+93}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d}}{d} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -1.55 \cdot 10^{-175}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 2.1 \cdot 10^{-221}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 2.3 \cdot 10^{+145}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{d}}{\frac{d}{b}} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* c b) (* d a)) (+ (* c c) (* d d)))))
   (if (<= d -2.2e+93)
     (- (/ (* c (/ b d)) d) (/ a d))
     (if (<= d -1.55e-175)
       t_0
       (if (<= d 2.1e-221)
         (/ b c)
         (if (<= d 2.3e+145) t_0 (- (/ (/ c d) (/ d b)) (/ a d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((c * b) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -2.2e+93) {
		tmp = ((c * (b / d)) / d) - (a / d);
	} else if (d <= -1.55e-175) {
		tmp = t_0;
	} else if (d <= 2.1e-221) {
		tmp = b / c;
	} else if (d <= 2.3e+145) {
		tmp = t_0;
	} else {
		tmp = ((c / d) / (d / 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) :: t_0
    real(8) :: tmp
    t_0 = ((c * b) - (d * a)) / ((c * c) + (d * d))
    if (d <= (-2.2d+93)) then
        tmp = ((c * (b / d)) / d) - (a / d)
    else if (d <= (-1.55d-175)) then
        tmp = t_0
    else if (d <= 2.1d-221) then
        tmp = b / c
    else if (d <= 2.3d+145) then
        tmp = t_0
    else
        tmp = ((c / d) / (d / b)) - (a / d)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((c * b) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -2.2e+93) {
		tmp = ((c * (b / d)) / d) - (a / d);
	} else if (d <= -1.55e-175) {
		tmp = t_0;
	} else if (d <= 2.1e-221) {
		tmp = b / c;
	} else if (d <= 2.3e+145) {
		tmp = t_0;
	} else {
		tmp = ((c / d) / (d / b)) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((c * b) - (d * a)) / ((c * c) + (d * d))
	tmp = 0
	if d <= -2.2e+93:
		tmp = ((c * (b / d)) / d) - (a / d)
	elif d <= -1.55e-175:
		tmp = t_0
	elif d <= 2.1e-221:
		tmp = b / c
	elif d <= 2.3e+145:
		tmp = t_0
	else:
		tmp = ((c / d) / (d / b)) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(c * b) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (d <= -2.2e+93)
		tmp = Float64(Float64(Float64(c * Float64(b / d)) / d) - Float64(a / d));
	elseif (d <= -1.55e-175)
		tmp = t_0;
	elseif (d <= 2.1e-221)
		tmp = Float64(b / c);
	elseif (d <= 2.3e+145)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(c / d) / Float64(d / b)) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((c * b) - (d * a)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (d <= -2.2e+93)
		tmp = ((c * (b / d)) / d) - (a / d);
	elseif (d <= -1.55e-175)
		tmp = t_0;
	elseif (d <= 2.1e-221)
		tmp = b / c;
	elseif (d <= 2.3e+145)
		tmp = t_0;
	else
		tmp = ((c / d) / (d / b)) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(c * b), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -2.2e+93], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -1.55e-175], t$95$0, If[LessEqual[d, 2.1e-221], N[(b / c), $MachinePrecision], If[LessEqual[d, 2.3e+145], t$95$0, N[(N[(N[(c / d), $MachinePrecision] / N[(d / b), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

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

Alternative 10: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-a}{d}\\ \mathbf{if}\;d \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -2.3 \cdot 10^{-12}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 2.35 \cdot 10^{-217}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{a \cdot \frac{d}{c}}{-c}\\ \mathbf{elif}\;d \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- a) d)))
   (if (<= d -2.8e+56)
     t_0
     (if (<= d -2.3e-12)
       (/ b c)
       (if (<= d -1e-70)
         t_0
         (if (<= d 2.35e-217)
           (/ b c)
           (if (<= d 1.9e-184)
             (/ (* a (/ d c)) (- c))
             (if (<= d 6.2e+34) (/ b c) t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = -a / d;
	double tmp;
	if (d <= -2.8e+56) {
		tmp = t_0;
	} else if (d <= -2.3e-12) {
		tmp = b / c;
	} else if (d <= -1e-70) {
		tmp = t_0;
	} else if (d <= 2.35e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a * (d / c)) / -c;
	} else if (d <= 6.2e+34) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -a / d
    if (d <= (-2.8d+56)) then
        tmp = t_0
    else if (d <= (-2.3d-12)) then
        tmp = b / c
    else if (d <= (-1d-70)) then
        tmp = t_0
    else if (d <= 2.35d-217) then
        tmp = b / c
    else if (d <= 1.9d-184) then
        tmp = (a * (d / c)) / -c
    else if (d <= 6.2d+34) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = -a / d;
	double tmp;
	if (d <= -2.8e+56) {
		tmp = t_0;
	} else if (d <= -2.3e-12) {
		tmp = b / c;
	} else if (d <= -1e-70) {
		tmp = t_0;
	} else if (d <= 2.35e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a * (d / c)) / -c;
	} else if (d <= 6.2e+34) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = -a / d
	tmp = 0
	if d <= -2.8e+56:
		tmp = t_0
	elif d <= -2.3e-12:
		tmp = b / c
	elif d <= -1e-70:
		tmp = t_0
	elif d <= 2.35e-217:
		tmp = b / c
	elif d <= 1.9e-184:
		tmp = (a * (d / c)) / -c
	elif d <= 6.2e+34:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(-a) / d)
	tmp = 0.0
	if (d <= -2.8e+56)
		tmp = t_0;
	elseif (d <= -2.3e-12)
		tmp = Float64(b / c);
	elseif (d <= -1e-70)
		tmp = t_0;
	elseif (d <= 2.35e-217)
		tmp = Float64(b / c);
	elseif (d <= 1.9e-184)
		tmp = Float64(Float64(a * Float64(d / c)) / Float64(-c));
	elseif (d <= 6.2e+34)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = -a / d;
	tmp = 0.0;
	if (d <= -2.8e+56)
		tmp = t_0;
	elseif (d <= -2.3e-12)
		tmp = b / c;
	elseif (d <= -1e-70)
		tmp = t_0;
	elseif (d <= 2.35e-217)
		tmp = b / c;
	elseif (d <= 1.9e-184)
		tmp = (a * (d / c)) / -c;
	elseif (d <= 6.2e+34)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[((-a) / d), $MachinePrecision]}, If[LessEqual[d, -2.8e+56], t$95$0, If[LessEqual[d, -2.3e-12], N[(b / c), $MachinePrecision], If[LessEqual[d, -1e-70], t$95$0, If[LessEqual[d, 2.35e-217], N[(b / c), $MachinePrecision], If[LessEqual[d, 1.9e-184], N[(N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision] / (-c)), $MachinePrecision], If[LessEqual[d, 6.2e+34], N[(b / c), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 11: 61.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-a}{d}\\ \mathbf{if}\;d \leq -2.4 \cdot 10^{+54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq -7 \cdot 10^{-14}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq -1 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 4.8 \cdot 10^{-217}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 1.9 \cdot 10^{-184}:\\ \;\;\;\;\frac{\frac{a}{c}}{\frac{-c}{d}}\\ \mathbf{elif}\;d \leq 2.8 \cdot 10^{+35}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- a) d)))
   (if (<= d -2.4e+54)
     t_0
     (if (<= d -7e-14)
       (/ b c)
       (if (<= d -1e-70)
         t_0
         (if (<= d 4.8e-217)
           (/ b c)
           (if (<= d 1.9e-184)
             (/ (/ a c) (/ (- c) d))
             (if (<= d 2.8e+35) (/ b c) t_0))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = -a / d;
	double tmp;
	if (d <= -2.4e+54) {
		tmp = t_0;
	} else if (d <= -7e-14) {
		tmp = b / c;
	} else if (d <= -1e-70) {
		tmp = t_0;
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 2.8e+35) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -a / d
    if (d <= (-2.4d+54)) then
        tmp = t_0
    else if (d <= (-7d-14)) then
        tmp = b / c
    else if (d <= (-1d-70)) then
        tmp = t_0
    else if (d <= 4.8d-217) then
        tmp = b / c
    else if (d <= 1.9d-184) then
        tmp = (a / c) / (-c / d)
    else if (d <= 2.8d+35) then
        tmp = b / c
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = -a / d;
	double tmp;
	if (d <= -2.4e+54) {
		tmp = t_0;
	} else if (d <= -7e-14) {
		tmp = b / c;
	} else if (d <= -1e-70) {
		tmp = t_0;
	} else if (d <= 4.8e-217) {
		tmp = b / c;
	} else if (d <= 1.9e-184) {
		tmp = (a / c) / (-c / d);
	} else if (d <= 2.8e+35) {
		tmp = b / c;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = -a / d
	tmp = 0
	if d <= -2.4e+54:
		tmp = t_0
	elif d <= -7e-14:
		tmp = b / c
	elif d <= -1e-70:
		tmp = t_0
	elif d <= 4.8e-217:
		tmp = b / c
	elif d <= 1.9e-184:
		tmp = (a / c) / (-c / d)
	elif d <= 2.8e+35:
		tmp = b / c
	else:
		tmp = t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(-a) / d)
	tmp = 0.0
	if (d <= -2.4e+54)
		tmp = t_0;
	elseif (d <= -7e-14)
		tmp = Float64(b / c);
	elseif (d <= -1e-70)
		tmp = t_0;
	elseif (d <= 4.8e-217)
		tmp = Float64(b / c);
	elseif (d <= 1.9e-184)
		tmp = Float64(Float64(a / c) / Float64(Float64(-c) / d));
	elseif (d <= 2.8e+35)
		tmp = Float64(b / c);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = -a / d;
	tmp = 0.0;
	if (d <= -2.4e+54)
		tmp = t_0;
	elseif (d <= -7e-14)
		tmp = b / c;
	elseif (d <= -1e-70)
		tmp = t_0;
	elseif (d <= 4.8e-217)
		tmp = b / c;
	elseif (d <= 1.9e-184)
		tmp = (a / c) / (-c / d);
	elseif (d <= 2.8e+35)
		tmp = b / c;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[((-a) / d), $MachinePrecision]}, If[LessEqual[d, -2.4e+54], t$95$0, If[LessEqual[d, -7e-14], N[(b / c), $MachinePrecision], If[LessEqual[d, -1e-70], t$95$0, If[LessEqual[d, 4.8e-217], N[(b / c), $MachinePrecision], If[LessEqual[d, 1.9e-184], N[(N[(a / c), $MachinePrecision] / N[((-c) / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2.8e+35], N[(b / c), $MachinePrecision], t$95$0]]]]]]]

Derivation

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

Alternative 12: 63.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.3 \cdot 10^{-26} \lor \neg \left(c \leq 3.6 \cdot 10^{+53}\right):\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= c -4.3e-26) (not (<= c 3.6e+53))) (/ b c) (/ (- a) d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((c <= -4.3e-26) || !(c <= 3.6e+53)) {
		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 <= (-4.3d-26)) .or. (.not. (c <= 3.6d+53))) 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 <= -4.3e-26) || !(c <= 3.6e+53)) {
		tmp = b / c;
	} else {
		tmp = -a / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (c <= -4.3e-26) or not (c <= 3.6e+53):
		tmp = b / c
	else:
		tmp = -a / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((c <= -4.3e-26) || !(c <= 3.6e+53))
		tmp = Float64(b / c);
	else
		tmp = Float64(Float64(-a) / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((c <= -4.3e-26) || ~((c <= 3.6e+53)))
		tmp = b / c;
	else
		tmp = -a / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[c, -4.3e-26], N[Not[LessEqual[c, 3.6e+53]], $MachinePrecision]], N[(b / c), $MachinePrecision], N[((-a) / d), $MachinePrecision]]

Derivation

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

Alternative 13: 11.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq 2.55 \cdot 10^{+123}:\\ \;\;\;\;\frac{a}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (if (<= d 2.55e+123) (/ a c) (/ a d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= 2.55e+123) {
		tmp = a / 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 <= 2.55d+123) then
        tmp = a / 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 <= 2.55e+123) {
		tmp = a / c;
	} else {
		tmp = a / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= 2.55e+123:
		tmp = a / c
	else:
		tmp = a / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= 2.55e+123)
		tmp = Float64(a / c);
	else
		tmp = Float64(a / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= 2.55e+123)
		tmp = a / c;
	else
		tmp = a / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, 2.55e+123], N[(a / c), $MachinePrecision], N[(a / d), $MachinePrecision]]

Derivation

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

Alternative 14: 44.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq 7 \cdot 10^{+165}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (if (<= d 7e+165) (/ b c) (/ a d)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= 7e+165) {
		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 (d <= 7d+165) 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 (d <= 7e+165) {
		tmp = b / c;
	} else {
		tmp = a / d;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= 7e+165:
		tmp = b / c
	else:
		tmp = a / d
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= 7e+165)
		tmp = Float64(b / c);
	else
		tmp = Float64(a / d);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= 7e+165)
		tmp = b / c;
	else
		tmp = a / d;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, 7e+165], N[(b / c), $MachinePrecision], N[(a / d), $MachinePrecision]]

Derivation

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

Alternative 15: 9.6% 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: 99.1% 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 2023347 
(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))))