fabs fraction 1

Percentage Accurate: 91.9% → 99.7%

Time: 6.8s

Alternatives: 11

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))

C

double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - ((x / y) * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = abs((((x + 4.0d0) / y) - ((x / y) * z)))
end function

Java

public static double code(double x, double y, double z) {
	return Math.abs((((x + 4.0) / y) - ((x / y) * z)));
}

Python

def code(x, y, z):
	return math.fabs((((x + 4.0) / y) - ((x / y) * z)))

Julia

function code(x, y, z)
	return abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(Float64(x / y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = abs((((x + 4.0) / y) - ((x / y) * z)));
end

Wolfram

code[x_, y_, z_] := N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Initial Program: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))

C

double code(double x, double y, double z) {
	return fabs((((x + 4.0) / y) - ((x / y) * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = abs((((x + 4.0d0) / y) - ((x / y) * z)))
end function

Java

public static double code(double x, double y, double z) {
	return Math.abs((((x + 4.0) / y) - ((x / y) * z)));
}

Python

def code(x, y, z):
	return math.fabs((((x + 4.0) / y) - ((x / y) * z)))

Julia

function code(x, y, z)
	return abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(Float64(x / y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = abs((((x + 4.0) / y) - ((x / y) * z)));
end

Wolfram

code[x_, y_, z_] := N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]

Alternative 1: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;y_m \leq 10^{+52}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y_m}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\mathsf{fma}\left(x, \frac{z}{y_m}, \frac{-4 - x}{y_m}\right)\right|\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (if (<= y_m 1e+52)
   (fabs (/ (- (+ 4.0 x) (* x z)) y_m))
   (fabs (fma x (/ z y_m) (/ (- -4.0 x) y_m)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double tmp;
	if (y_m <= 1e+52) {
		tmp = fabs((((4.0 + x) - (x * z)) / y_m));
	} else {
		tmp = fabs(fma(x, (z / y_m), ((-4.0 - x) / y_m)));
	}
	return tmp;
}

Julia

y_m = abs(y)
function code(x, y_m, z)
	tmp = 0.0
	if (y_m <= 1e+52)
		tmp = abs(Float64(Float64(Float64(4.0 + x) - Float64(x * z)) / y_m));
	else
		tmp = abs(fma(x, Float64(z / y_m), Float64(Float64(-4.0 - x) / y_m)));
	end
	return tmp
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := If[LessEqual[y$95$m, 1e+52], N[Abs[N[(N[(N[(4.0 + x), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y$95$m), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x * N[(z / y$95$m), $MachinePrecision] + N[(N[(-4.0 - x), $MachinePrecision] / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 2: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \left|\frac{4}{y_m}\right|\\ t_1 := \left|\frac{x}{y_m}\right|\\ t_2 := \left|z \cdot \frac{x}{y_m}\right|\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+55}:\\ \;\;\;\;\left|x \cdot \frac{z}{y_m}\right|\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (let* ((t_0 (fabs (/ 4.0 y_m)))
        (t_1 (fabs (/ x y_m)))
        (t_2 (fabs (* z (/ x y_m)))))
   (if (<= x -4.8e+152)
     t_1
     (if (<= x -2.35e-35)
       t_2
       (if (<= x -1.9e-135)
         t_0
         (if (<= x -3.1e-146)
           t_2
           (if (<= x 1.2e-39)
             t_0
             (if (<= x 2.35e+55) (fabs (* x (/ z y_m))) t_1))))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double t_0 = fabs((4.0 / y_m));
	double t_1 = fabs((x / y_m));
	double t_2 = fabs((z * (x / y_m)));
	double tmp;
	if (x <= -4.8e+152) {
		tmp = t_1;
	} else if (x <= -2.35e-35) {
		tmp = t_2;
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -3.1e-146) {
		tmp = t_2;
	} else if (x <= 1.2e-39) {
		tmp = t_0;
	} else if (x <= 2.35e+55) {
		tmp = fabs((x * (z / y_m)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = abs((4.0d0 / y_m))
    t_1 = abs((x / y_m))
    t_2 = abs((z * (x / y_m)))
    if (x <= (-4.8d+152)) then
        tmp = t_1
    else if (x <= (-2.35d-35)) then
        tmp = t_2
    else if (x <= (-1.9d-135)) then
        tmp = t_0
    else if (x <= (-3.1d-146)) then
        tmp = t_2
    else if (x <= 1.2d-39) then
        tmp = t_0
    else if (x <= 2.35d+55) then
        tmp = abs((x * (z / y_m)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double t_0 = Math.abs((4.0 / y_m));
	double t_1 = Math.abs((x / y_m));
	double t_2 = Math.abs((z * (x / y_m)));
	double tmp;
	if (x <= -4.8e+152) {
		tmp = t_1;
	} else if (x <= -2.35e-35) {
		tmp = t_2;
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -3.1e-146) {
		tmp = t_2;
	} else if (x <= 1.2e-39) {
		tmp = t_0;
	} else if (x <= 2.35e+55) {
		tmp = Math.abs((x * (z / y_m)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	t_0 = math.fabs((4.0 / y_m))
	t_1 = math.fabs((x / y_m))
	t_2 = math.fabs((z * (x / y_m)))
	tmp = 0
	if x <= -4.8e+152:
		tmp = t_1
	elif x <= -2.35e-35:
		tmp = t_2
	elif x <= -1.9e-135:
		tmp = t_0
	elif x <= -3.1e-146:
		tmp = t_2
	elif x <= 1.2e-39:
		tmp = t_0
	elif x <= 2.35e+55:
		tmp = math.fabs((x * (z / y_m)))
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	t_0 = abs(Float64(4.0 / y_m))
	t_1 = abs(Float64(x / y_m))
	t_2 = abs(Float64(z * Float64(x / y_m)))
	tmp = 0.0
	if (x <= -4.8e+152)
		tmp = t_1;
	elseif (x <= -2.35e-35)
		tmp = t_2;
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -3.1e-146)
		tmp = t_2;
	elseif (x <= 1.2e-39)
		tmp = t_0;
	elseif (x <= 2.35e+55)
		tmp = abs(Float64(x * Float64(z / y_m)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	t_0 = abs((4.0 / y_m));
	t_1 = abs((x / y_m));
	t_2 = abs((z * (x / y_m)));
	tmp = 0.0;
	if (x <= -4.8e+152)
		tmp = t_1;
	elseif (x <= -2.35e-35)
		tmp = t_2;
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -3.1e-146)
		tmp = t_2;
	elseif (x <= 1.2e-39)
		tmp = t_0;
	elseif (x <= 2.35e+55)
		tmp = abs((x * (z / y_m)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := Block[{t$95$0 = N[Abs[N[(4.0 / y$95$m), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Abs[N[(z * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -4.8e+152], t$95$1, If[LessEqual[x, -2.35e-35], t$95$2, If[LessEqual[x, -1.9e-135], t$95$0, If[LessEqual[x, -3.1e-146], t$95$2, If[LessEqual[x, 1.2e-39], t$95$0, If[LessEqual[x, 2.35e+55], N[Abs[N[(x * N[(z / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$1]]]]]]]]]

Derivation

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

Alternative 3: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \left|\frac{4}{y_m}\right|\\ t_1 := \left|\frac{x}{y_m}\right|\\ t_2 := \left|z \cdot \frac{x}{y_m}\right|\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.95 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+55}:\\ \;\;\;\;\left|\frac{x}{\frac{y_m}{z}}\right|\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (let* ((t_0 (fabs (/ 4.0 y_m)))
        (t_1 (fabs (/ x y_m)))
        (t_2 (fabs (* z (/ x y_m)))))
   (if (<= x -8.2e+152)
     t_1
     (if (<= x -1.7e-30)
       t_2
       (if (<= x -1.9e-135)
         t_0
         (if (<= x -3.1e-146)
           t_2
           (if (<= x 1.95e-39)
             t_0
             (if (<= x 1.2e+55) (fabs (/ x (/ y_m z))) t_1))))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double t_0 = fabs((4.0 / y_m));
	double t_1 = fabs((x / y_m));
	double t_2 = fabs((z * (x / y_m)));
	double tmp;
	if (x <= -8.2e+152) {
		tmp = t_1;
	} else if (x <= -1.7e-30) {
		tmp = t_2;
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -3.1e-146) {
		tmp = t_2;
	} else if (x <= 1.95e-39) {
		tmp = t_0;
	} else if (x <= 1.2e+55) {
		tmp = fabs((x / (y_m / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = abs((4.0d0 / y_m))
    t_1 = abs((x / y_m))
    t_2 = abs((z * (x / y_m)))
    if (x <= (-8.2d+152)) then
        tmp = t_1
    else if (x <= (-1.7d-30)) then
        tmp = t_2
    else if (x <= (-1.9d-135)) then
        tmp = t_0
    else if (x <= (-3.1d-146)) then
        tmp = t_2
    else if (x <= 1.95d-39) then
        tmp = t_0
    else if (x <= 1.2d+55) then
        tmp = abs((x / (y_m / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double t_0 = Math.abs((4.0 / y_m));
	double t_1 = Math.abs((x / y_m));
	double t_2 = Math.abs((z * (x / y_m)));
	double tmp;
	if (x <= -8.2e+152) {
		tmp = t_1;
	} else if (x <= -1.7e-30) {
		tmp = t_2;
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -3.1e-146) {
		tmp = t_2;
	} else if (x <= 1.95e-39) {
		tmp = t_0;
	} else if (x <= 1.2e+55) {
		tmp = Math.abs((x / (y_m / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	t_0 = math.fabs((4.0 / y_m))
	t_1 = math.fabs((x / y_m))
	t_2 = math.fabs((z * (x / y_m)))
	tmp = 0
	if x <= -8.2e+152:
		tmp = t_1
	elif x <= -1.7e-30:
		tmp = t_2
	elif x <= -1.9e-135:
		tmp = t_0
	elif x <= -3.1e-146:
		tmp = t_2
	elif x <= 1.95e-39:
		tmp = t_0
	elif x <= 1.2e+55:
		tmp = math.fabs((x / (y_m / z)))
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	t_0 = abs(Float64(4.0 / y_m))
	t_1 = abs(Float64(x / y_m))
	t_2 = abs(Float64(z * Float64(x / y_m)))
	tmp = 0.0
	if (x <= -8.2e+152)
		tmp = t_1;
	elseif (x <= -1.7e-30)
		tmp = t_2;
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -3.1e-146)
		tmp = t_2;
	elseif (x <= 1.95e-39)
		tmp = t_0;
	elseif (x <= 1.2e+55)
		tmp = abs(Float64(x / Float64(y_m / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	t_0 = abs((4.0 / y_m));
	t_1 = abs((x / y_m));
	t_2 = abs((z * (x / y_m)));
	tmp = 0.0;
	if (x <= -8.2e+152)
		tmp = t_1;
	elseif (x <= -1.7e-30)
		tmp = t_2;
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -3.1e-146)
		tmp = t_2;
	elseif (x <= 1.95e-39)
		tmp = t_0;
	elseif (x <= 1.2e+55)
		tmp = abs((x / (y_m / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := Block[{t$95$0 = N[Abs[N[(4.0 / y$95$m), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Abs[N[(z * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -8.2e+152], t$95$1, If[LessEqual[x, -1.7e-30], t$95$2, If[LessEqual[x, -1.9e-135], t$95$0, If[LessEqual[x, -3.1e-146], t$95$2, If[LessEqual[x, 1.95e-39], t$95$0, If[LessEqual[x, 1.2e+55], N[Abs[N[(x / N[(y$95$m / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$1]]]]]]]]]

Derivation

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

Alternative 4: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \left|\frac{4}{y_m}\right|\\ t_1 := \left|\frac{x}{y_m}\right|\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{-34}:\\ \;\;\;\;\left|z \cdot \frac{x}{y_m}\right|\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-146}:\\ \;\;\;\;\left|\frac{z}{\frac{y_m}{x}}\right|\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+55}:\\ \;\;\;\;\left|\frac{x}{\frac{y_m}{z}}\right|\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (let* ((t_0 (fabs (/ 4.0 y_m))) (t_1 (fabs (/ x y_m))))
   (if (<= x -1.15e+153)
     t_1
     (if (<= x -4.9e-34)
       (fabs (* z (/ x y_m)))
       (if (<= x -1.9e-135)
         t_0
         (if (<= x -3.1e-146)
           (fabs (/ z (/ y_m x)))
           (if (<= x 1.15e-39)
             t_0
             (if (<= x 9.5e+55) (fabs (/ x (/ y_m z))) t_1))))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double t_0 = fabs((4.0 / y_m));
	double t_1 = fabs((x / y_m));
	double tmp;
	if (x <= -1.15e+153) {
		tmp = t_1;
	} else if (x <= -4.9e-34) {
		tmp = fabs((z * (x / y_m)));
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -3.1e-146) {
		tmp = fabs((z / (y_m / x)));
	} else if (x <= 1.15e-39) {
		tmp = t_0;
	} else if (x <= 9.5e+55) {
		tmp = fabs((x / (y_m / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = abs((4.0d0 / y_m))
    t_1 = abs((x / y_m))
    if (x <= (-1.15d+153)) then
        tmp = t_1
    else if (x <= (-4.9d-34)) then
        tmp = abs((z * (x / y_m)))
    else if (x <= (-1.9d-135)) then
        tmp = t_0
    else if (x <= (-3.1d-146)) then
        tmp = abs((z / (y_m / x)))
    else if (x <= 1.15d-39) then
        tmp = t_0
    else if (x <= 9.5d+55) then
        tmp = abs((x / (y_m / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double t_0 = Math.abs((4.0 / y_m));
	double t_1 = Math.abs((x / y_m));
	double tmp;
	if (x <= -1.15e+153) {
		tmp = t_1;
	} else if (x <= -4.9e-34) {
		tmp = Math.abs((z * (x / y_m)));
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -3.1e-146) {
		tmp = Math.abs((z / (y_m / x)));
	} else if (x <= 1.15e-39) {
		tmp = t_0;
	} else if (x <= 9.5e+55) {
		tmp = Math.abs((x / (y_m / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	t_0 = math.fabs((4.0 / y_m))
	t_1 = math.fabs((x / y_m))
	tmp = 0
	if x <= -1.15e+153:
		tmp = t_1
	elif x <= -4.9e-34:
		tmp = math.fabs((z * (x / y_m)))
	elif x <= -1.9e-135:
		tmp = t_0
	elif x <= -3.1e-146:
		tmp = math.fabs((z / (y_m / x)))
	elif x <= 1.15e-39:
		tmp = t_0
	elif x <= 9.5e+55:
		tmp = math.fabs((x / (y_m / z)))
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	t_0 = abs(Float64(4.0 / y_m))
	t_1 = abs(Float64(x / y_m))
	tmp = 0.0
	if (x <= -1.15e+153)
		tmp = t_1;
	elseif (x <= -4.9e-34)
		tmp = abs(Float64(z * Float64(x / y_m)));
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -3.1e-146)
		tmp = abs(Float64(z / Float64(y_m / x)));
	elseif (x <= 1.15e-39)
		tmp = t_0;
	elseif (x <= 9.5e+55)
		tmp = abs(Float64(x / Float64(y_m / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	t_0 = abs((4.0 / y_m));
	t_1 = abs((x / y_m));
	tmp = 0.0;
	if (x <= -1.15e+153)
		tmp = t_1;
	elseif (x <= -4.9e-34)
		tmp = abs((z * (x / y_m)));
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -3.1e-146)
		tmp = abs((z / (y_m / x)));
	elseif (x <= 1.15e-39)
		tmp = t_0;
	elseif (x <= 9.5e+55)
		tmp = abs((x / (y_m / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := Block[{t$95$0 = N[Abs[N[(4.0 / y$95$m), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -1.15e+153], t$95$1, If[LessEqual[x, -4.9e-34], N[Abs[N[(z * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, -1.9e-135], t$95$0, If[LessEqual[x, -3.1e-146], N[Abs[N[(z / N[(y$95$m / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.15e-39], t$95$0, If[LessEqual[x, 9.5e+55], N[Abs[N[(x / N[(y$95$m / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$1]]]]]]]]

Derivation

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

Alternative 5: 68.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \left|\frac{4}{y_m}\right|\\ t_1 := \left|\frac{x}{y_m}\right|\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-38}:\\ \;\;\;\;\left|z \cdot \frac{x}{y_m}\right|\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-147}:\\ \;\;\;\;\left|\frac{x \cdot z}{y_m}\right|\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+55}:\\ \;\;\;\;\left|\frac{x}{\frac{y_m}{z}}\right|\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (let* ((t_0 (fabs (/ 4.0 y_m))) (t_1 (fabs (/ x y_m))))
   (if (<= x -5.8e+152)
     t_1
     (if (<= x -1.35e-38)
       (fabs (* z (/ x y_m)))
       (if (<= x -1.9e-135)
         t_0
         (if (<= x -1.8e-147)
           (fabs (/ (* x z) y_m))
           (if (<= x 1.26e-39)
             t_0
             (if (<= x 1.35e+55) (fabs (/ x (/ y_m z))) t_1))))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double t_0 = fabs((4.0 / y_m));
	double t_1 = fabs((x / y_m));
	double tmp;
	if (x <= -5.8e+152) {
		tmp = t_1;
	} else if (x <= -1.35e-38) {
		tmp = fabs((z * (x / y_m)));
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -1.8e-147) {
		tmp = fabs(((x * z) / y_m));
	} else if (x <= 1.26e-39) {
		tmp = t_0;
	} else if (x <= 1.35e+55) {
		tmp = fabs((x / (y_m / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = abs((4.0d0 / y_m))
    t_1 = abs((x / y_m))
    if (x <= (-5.8d+152)) then
        tmp = t_1
    else if (x <= (-1.35d-38)) then
        tmp = abs((z * (x / y_m)))
    else if (x <= (-1.9d-135)) then
        tmp = t_0
    else if (x <= (-1.8d-147)) then
        tmp = abs(((x * z) / y_m))
    else if (x <= 1.26d-39) then
        tmp = t_0
    else if (x <= 1.35d+55) then
        tmp = abs((x / (y_m / z)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double t_0 = Math.abs((4.0 / y_m));
	double t_1 = Math.abs((x / y_m));
	double tmp;
	if (x <= -5.8e+152) {
		tmp = t_1;
	} else if (x <= -1.35e-38) {
		tmp = Math.abs((z * (x / y_m)));
	} else if (x <= -1.9e-135) {
		tmp = t_0;
	} else if (x <= -1.8e-147) {
		tmp = Math.abs(((x * z) / y_m));
	} else if (x <= 1.26e-39) {
		tmp = t_0;
	} else if (x <= 1.35e+55) {
		tmp = Math.abs((x / (y_m / z)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	t_0 = math.fabs((4.0 / y_m))
	t_1 = math.fabs((x / y_m))
	tmp = 0
	if x <= -5.8e+152:
		tmp = t_1
	elif x <= -1.35e-38:
		tmp = math.fabs((z * (x / y_m)))
	elif x <= -1.9e-135:
		tmp = t_0
	elif x <= -1.8e-147:
		tmp = math.fabs(((x * z) / y_m))
	elif x <= 1.26e-39:
		tmp = t_0
	elif x <= 1.35e+55:
		tmp = math.fabs((x / (y_m / z)))
	else:
		tmp = t_1
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	t_0 = abs(Float64(4.0 / y_m))
	t_1 = abs(Float64(x / y_m))
	tmp = 0.0
	if (x <= -5.8e+152)
		tmp = t_1;
	elseif (x <= -1.35e-38)
		tmp = abs(Float64(z * Float64(x / y_m)));
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -1.8e-147)
		tmp = abs(Float64(Float64(x * z) / y_m));
	elseif (x <= 1.26e-39)
		tmp = t_0;
	elseif (x <= 1.35e+55)
		tmp = abs(Float64(x / Float64(y_m / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	t_0 = abs((4.0 / y_m));
	t_1 = abs((x / y_m));
	tmp = 0.0;
	if (x <= -5.8e+152)
		tmp = t_1;
	elseif (x <= -1.35e-38)
		tmp = abs((z * (x / y_m)));
	elseif (x <= -1.9e-135)
		tmp = t_0;
	elseif (x <= -1.8e-147)
		tmp = abs(((x * z) / y_m));
	elseif (x <= 1.26e-39)
		tmp = t_0;
	elseif (x <= 1.35e+55)
		tmp = abs((x / (y_m / z)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := Block[{t$95$0 = N[Abs[N[(4.0 / y$95$m), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -5.8e+152], t$95$1, If[LessEqual[x, -1.35e-38], N[Abs[N[(z * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, -1.9e-135], t$95$0, If[LessEqual[x, -1.8e-147], N[Abs[N[(N[(x * z), $MachinePrecision] / y$95$m), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.26e-39], t$95$0, If[LessEqual[x, 1.35e+55], N[Abs[N[(x / N[(y$95$m / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], t$95$1]]]]]]]]

Derivation

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

Alternative 6: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} t_0 := \left|\frac{x}{y_m}\right|\\ t_1 := \left|x \cdot \frac{z}{y_m}\right|\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-39}:\\ \;\;\;\;\left|\frac{4}{y_m}\right|\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y_m))) (t_1 (fabs (* x (/ z y_m)))))
   (if (<= x -2.2e+138)
     t_0
     (if (<= x -2.35e-35)
       t_1
       (if (<= x 1.16e-39) (fabs (/ 4.0 y_m)) (if (<= x 5.8e+55) t_1 t_0))))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double t_0 = fabs((x / y_m));
	double t_1 = fabs((x * (z / y_m)));
	double tmp;
	if (x <= -2.2e+138) {
		tmp = t_0;
	} else if (x <= -2.35e-35) {
		tmp = t_1;
	} else if (x <= 1.16e-39) {
		tmp = fabs((4.0 / y_m));
	} else if (x <= 5.8e+55) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = abs((x / y_m))
    t_1 = abs((x * (z / y_m)))
    if (x <= (-2.2d+138)) then
        tmp = t_0
    else if (x <= (-2.35d-35)) then
        tmp = t_1
    else if (x <= 1.16d-39) then
        tmp = abs((4.0d0 / y_m))
    else if (x <= 5.8d+55) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double t_0 = Math.abs((x / y_m));
	double t_1 = Math.abs((x * (z / y_m)));
	double tmp;
	if (x <= -2.2e+138) {
		tmp = t_0;
	} else if (x <= -2.35e-35) {
		tmp = t_1;
	} else if (x <= 1.16e-39) {
		tmp = Math.abs((4.0 / y_m));
	} else if (x <= 5.8e+55) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	t_0 = math.fabs((x / y_m))
	t_1 = math.fabs((x * (z / y_m)))
	tmp = 0
	if x <= -2.2e+138:
		tmp = t_0
	elif x <= -2.35e-35:
		tmp = t_1
	elif x <= 1.16e-39:
		tmp = math.fabs((4.0 / y_m))
	elif x <= 5.8e+55:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	t_0 = abs(Float64(x / y_m))
	t_1 = abs(Float64(x * Float64(z / y_m)))
	tmp = 0.0
	if (x <= -2.2e+138)
		tmp = t_0;
	elseif (x <= -2.35e-35)
		tmp = t_1;
	elseif (x <= 1.16e-39)
		tmp = abs(Float64(4.0 / y_m));
	elseif (x <= 5.8e+55)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	t_0 = abs((x / y_m));
	t_1 = abs((x * (z / y_m)));
	tmp = 0.0;
	if (x <= -2.2e+138)
		tmp = t_0;
	elseif (x <= -2.35e-35)
		tmp = t_1;
	elseif (x <= 1.16e-39)
		tmp = abs((4.0 / y_m));
	elseif (x <= 5.8e+55)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := Block[{t$95$0 = N[Abs[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(x * N[(z / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -2.2e+138], t$95$0, If[LessEqual[x, -2.35e-35], t$95$1, If[LessEqual[x, 1.16e-39], N[Abs[N[(4.0 / y$95$m), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 5.8e+55], t$95$1, t$95$0]]]]]]

Derivation

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

Alternative 7: 84.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;\left|z \cdot \frac{x}{y_m} - \frac{x}{y_m}\right|\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+108}:\\ \;\;\;\;\left|\frac{-4 - x}{y_m}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x \cdot z}{y_m}\right|\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (if (<= z -1.2e-5)
   (fabs (- (* z (/ x y_m)) (/ x y_m)))
   (if (<= z 2e+108) (fabs (/ (- -4.0 x) y_m)) (fabs (/ (* x z) y_m)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double tmp;
	if (z <= -1.2e-5) {
		tmp = fabs(((z * (x / y_m)) - (x / y_m)));
	} else if (z <= 2e+108) {
		tmp = fabs(((-4.0 - x) / y_m));
	} else {
		tmp = fabs(((x * z) / y_m));
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.2d-5)) then
        tmp = abs(((z * (x / y_m)) - (x / y_m)))
    else if (z <= 2d+108) then
        tmp = abs((((-4.0d0) - x) / y_m))
    else
        tmp = abs(((x * z) / y_m))
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double tmp;
	if (z <= -1.2e-5) {
		tmp = Math.abs(((z * (x / y_m)) - (x / y_m)));
	} else if (z <= 2e+108) {
		tmp = Math.abs(((-4.0 - x) / y_m));
	} else {
		tmp = Math.abs(((x * z) / y_m));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	tmp = 0
	if z <= -1.2e-5:
		tmp = math.fabs(((z * (x / y_m)) - (x / y_m)))
	elif z <= 2e+108:
		tmp = math.fabs(((-4.0 - x) / y_m))
	else:
		tmp = math.fabs(((x * z) / y_m))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	tmp = 0.0
	if (z <= -1.2e-5)
		tmp = abs(Float64(Float64(z * Float64(x / y_m)) - Float64(x / y_m)));
	elseif (z <= 2e+108)
		tmp = abs(Float64(Float64(-4.0 - x) / y_m));
	else
		tmp = abs(Float64(Float64(x * z) / y_m));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	tmp = 0.0;
	if (z <= -1.2e-5)
		tmp = abs(((z * (x / y_m)) - (x / y_m)));
	elseif (z <= 2e+108)
		tmp = abs(((-4.0 - x) / y_m));
	else
		tmp = abs(((x * z) / y_m));
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := If[LessEqual[z, -1.2e-5], N[Abs[N[(N[(z * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision] - N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 2e+108], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y$95$m), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x * z), $MachinePrecision] / y$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 8: 83.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+144}:\\ \;\;\;\;\left|z \cdot \frac{x}{y_m}\right|\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+108}:\\ \;\;\;\;\left|\frac{-4 - x}{y_m}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x \cdot z}{y_m}\right|\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (if (<= z -4.2e+144)
   (fabs (* z (/ x y_m)))
   (if (<= z 3.5e+108) (fabs (/ (- -4.0 x) y_m)) (fabs (/ (* x z) y_m)))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double tmp;
	if (z <= -4.2e+144) {
		tmp = fabs((z * (x / y_m)));
	} else if (z <= 3.5e+108) {
		tmp = fabs(((-4.0 - x) / y_m));
	} else {
		tmp = fabs(((x * z) / y_m));
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.2d+144)) then
        tmp = abs((z * (x / y_m)))
    else if (z <= 3.5d+108) then
        tmp = abs((((-4.0d0) - x) / y_m))
    else
        tmp = abs(((x * z) / y_m))
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double tmp;
	if (z <= -4.2e+144) {
		tmp = Math.abs((z * (x / y_m)));
	} else if (z <= 3.5e+108) {
		tmp = Math.abs(((-4.0 - x) / y_m));
	} else {
		tmp = Math.abs(((x * z) / y_m));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	tmp = 0
	if z <= -4.2e+144:
		tmp = math.fabs((z * (x / y_m)))
	elif z <= 3.5e+108:
		tmp = math.fabs(((-4.0 - x) / y_m))
	else:
		tmp = math.fabs(((x * z) / y_m))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	tmp = 0.0
	if (z <= -4.2e+144)
		tmp = abs(Float64(z * Float64(x / y_m)));
	elseif (z <= 3.5e+108)
		tmp = abs(Float64(Float64(-4.0 - x) / y_m));
	else
		tmp = abs(Float64(Float64(x * z) / y_m));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	tmp = 0.0;
	if (z <= -4.2e+144)
		tmp = abs((z * (x / y_m)));
	elseif (z <= 3.5e+108)
		tmp = abs(((-4.0 - x) / y_m));
	else
		tmp = abs(((x * z) / y_m));
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := If[LessEqual[z, -4.2e+144], N[Abs[N[(z * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 3.5e+108], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y$95$m), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x * z), $MachinePrecision] / y$95$m), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 9: 95.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \left|\frac{\left(4 + x\right) - x \cdot z}{y_m}\right| \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z) :precision binary64 (fabs (/ (- (+ 4.0 x) (* x z)) y_m)))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	return fabs((((4.0 + x) - (x * z)) / y_m));
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = abs((((4.0d0 + x) - (x * z)) / y_m))
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	return Math.abs((((4.0 + x) - (x * z)) / y_m));
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	return math.fabs((((4.0 + x) - (x * z)) / y_m))

Julia

y_m = abs(y)
function code(x, y_m, z)
	return abs(Float64(Float64(Float64(4.0 + x) - Float64(x * z)) / y_m))
end

MATLAB

y_m = abs(y);
function tmp = code(x, y_m, z)
	tmp = abs((((4.0 + x) - (x * z)) / y_m));
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := N[Abs[N[(N[(N[(4.0 + x), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y$95$m), $MachinePrecision]], $MachinePrecision]

Derivation

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

Alternative 10: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y_m}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y_m}\right|\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z)
 :precision binary64
 (if (or (<= x -1.5) (not (<= x 4.0))) (fabs (/ x y_m)) (fabs (/ 4.0 y_m))))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	double tmp;
	if ((x <= -1.5) || !(x <= 4.0)) {
		tmp = fabs((x / y_m));
	} else {
		tmp = fabs((4.0 / y_m));
	}
	return tmp;
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.5d0)) .or. (.not. (x <= 4.0d0))) then
        tmp = abs((x / y_m))
    else
        tmp = abs((4.0d0 / y_m))
    end if
    code = tmp
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	double tmp;
	if ((x <= -1.5) || !(x <= 4.0)) {
		tmp = Math.abs((x / y_m));
	} else {
		tmp = Math.abs((4.0 / y_m));
	}
	return tmp;
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	tmp = 0
	if (x <= -1.5) or not (x <= 4.0):
		tmp = math.fabs((x / y_m))
	else:
		tmp = math.fabs((4.0 / y_m))
	return tmp

Julia

y_m = abs(y)
function code(x, y_m, z)
	tmp = 0.0
	if ((x <= -1.5) || !(x <= 4.0))
		tmp = abs(Float64(x / y_m));
	else
		tmp = abs(Float64(4.0 / y_m));
	end
	return tmp
end

MATLAB

y_m = abs(y);
function tmp_2 = code(x, y_m, z)
	tmp = 0.0;
	if ((x <= -1.5) || ~((x <= 4.0)))
		tmp = abs((x / y_m));
	else
		tmp = abs((4.0 / y_m));
	end
	tmp_2 = tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := If[Or[LessEqual[x, -1.5], N[Not[LessEqual[x, 4.0]], $MachinePrecision]], N[Abs[N[(x / y$95$m), $MachinePrecision]], $MachinePrecision], N[Abs[N[(4.0 / y$95$m), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 11: 40.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ \left|\frac{4}{y_m}\right| \end{array} \]

FPCore

y_m = (fabs.f64 y)
(FPCore (x y_m z) :precision binary64 (fabs (/ 4.0 y_m)))

C

y_m = fabs(y);
double code(double x, double y_m, double z) {
	return fabs((4.0 / y_m));
}

Fortran

y_m = abs(y)
real(8) function code(x, y_m, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = abs((4.0d0 / y_m))
end function

Java

y_m = Math.abs(y);
public static double code(double x, double y_m, double z) {
	return Math.abs((4.0 / y_m));
}

Python

y_m = math.fabs(y)
def code(x, y_m, z):
	return math.fabs((4.0 / y_m))

Julia

y_m = abs(y)
function code(x, y_m, z)
	return abs(Float64(4.0 / y_m))
end

MATLAB

y_m = abs(y);
function tmp = code(x, y_m, z)
	tmp = abs((4.0 / y_m));
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z_] := N[Abs[N[(4.0 / y$95$m), $MachinePrecision]], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2023343 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))