fabs fraction 1

Percentage Accurate: 91.7% → 97.8%

Time: 5.7s

Alternatives: 7

Speedup: 1.0×

• 20.5% 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: 91.7% 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: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 10^{-34}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\mathsf{fma}\left(x, \frac{z}{y}, \frac{-4 - x}{y}\right)\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1e-34)
   (fabs (/ (- (+ 4.0 x) (* x z)) y))
   (fabs (fma x (/ z y) (/ (- -4.0 x) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1e-34) {
		tmp = fabs((((4.0 + x) - (x * z)) / y));
	} else {
		tmp = fabs(fma(x, (z / y), ((-4.0 - x) / y)));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1e-34)
		tmp = abs(Float64(Float64(Float64(4.0 + x) - Float64(x * z)) / y));
	else
		tmp = abs(fma(x, Float64(z / y), Float64(Float64(-4.0 - x) / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1e-34], N[Abs[N[(N[(N[(4.0 + x), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x * N[(z / y), $MachinePrecision] + N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 2: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ t_1 := \left|z \cdot \frac{x}{y}\right|\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+160}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y))) (t_1 (fabs (* z (/ x y)))))
   (if (<= x -7.5e+81)
     t_0
     (if (<= x -6e+44)
       t_1
       (if (<= x -1.5)
         t_0
         (if (<= x 4.0) (fabs (/ 4.0 y)) (if (<= x 4.5e+160) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = fabs((x / y));
	double t_1 = fabs((z * (x / y)));
	double tmp;
	if (x <= -7.5e+81) {
		tmp = t_0;
	} else if (x <= -6e+44) {
		tmp = t_1;
	} else if (x <= -1.5) {
		tmp = t_0;
	} else if (x <= 4.0) {
		tmp = fabs((4.0 / y));
	} else if (x <= 4.5e+160) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = abs((x / y))
    t_1 = abs((z * (x / y)))
    if (x <= (-7.5d+81)) then
        tmp = t_0
    else if (x <= (-6d+44)) then
        tmp = t_1
    else if (x <= (-1.5d0)) then
        tmp = t_0
    else if (x <= 4.0d0) then
        tmp = abs((4.0d0 / y))
    else if (x <= 4.5d+160) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.abs((x / y));
	double t_1 = Math.abs((z * (x / y)));
	double tmp;
	if (x <= -7.5e+81) {
		tmp = t_0;
	} else if (x <= -6e+44) {
		tmp = t_1;
	} else if (x <= -1.5) {
		tmp = t_0;
	} else if (x <= 4.0) {
		tmp = Math.abs((4.0 / y));
	} else if (x <= 4.5e+160) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.fabs((x / y))
	t_1 = math.fabs((z * (x / y)))
	tmp = 0
	if x <= -7.5e+81:
		tmp = t_0
	elif x <= -6e+44:
		tmp = t_1
	elif x <= -1.5:
		tmp = t_0
	elif x <= 4.0:
		tmp = math.fabs((4.0 / y))
	elif x <= 4.5e+160:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = abs(Float64(x / y))
	t_1 = abs(Float64(z * Float64(x / y)))
	tmp = 0.0
	if (x <= -7.5e+81)
		tmp = t_0;
	elseif (x <= -6e+44)
		tmp = t_1;
	elseif (x <= -1.5)
		tmp = t_0;
	elseif (x <= 4.0)
		tmp = abs(Float64(4.0 / y));
	elseif (x <= 4.5e+160)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = abs((x / y));
	t_1 = abs((z * (x / y)));
	tmp = 0.0;
	if (x <= -7.5e+81)
		tmp = t_0;
	elseif (x <= -6e+44)
		tmp = t_1;
	elseif (x <= -1.5)
		tmp = t_0;
	elseif (x <= 4.0)
		tmp = abs((4.0 / y));
	elseif (x <= 4.5e+160)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -7.5e+81], t$95$0, If[LessEqual[x, -6e+44], t$95$1, If[LessEqual[x, -1.5], t$95$0, If[LessEqual[x, 4.0], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 4.5e+160], t$95$0, t$95$1]]]]]]]

Derivation

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

Alternative 3: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+63}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+115}:\\ \;\;\;\;\left|\frac{4}{y} + \frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.6e+63)
   (fabs (/ z (/ y x)))
   (if (<= z 1.9e+115) (fabs (+ (/ 4.0 y) (/ x y))) (fabs (/ x (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.6e+63) {
		tmp = fabs((z / (y / x)));
	} else if (z <= 1.9e+115) {
		tmp = fabs(((4.0 / y) + (x / y)));
	} else {
		tmp = fabs((x / (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9.6d+63)) then
        tmp = abs((z / (y / x)))
    else if (z <= 1.9d+115) then
        tmp = abs(((4.0d0 / y) + (x / y)))
    else
        tmp = abs((x / (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.6e+63) {
		tmp = Math.abs((z / (y / x)));
	} else if (z <= 1.9e+115) {
		tmp = Math.abs(((4.0 / y) + (x / y)));
	} else {
		tmp = Math.abs((x / (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.6e+63:
		tmp = math.fabs((z / (y / x)))
	elif z <= 1.9e+115:
		tmp = math.fabs(((4.0 / y) + (x / y)))
	else:
		tmp = math.fabs((x / (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.6e+63)
		tmp = abs(Float64(z / Float64(y / x)));
	elseif (z <= 1.9e+115)
		tmp = abs(Float64(Float64(4.0 / y) + Float64(x / y)));
	else
		tmp = abs(Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.6e+63)
		tmp = abs((z / (y / x)));
	elseif (z <= 1.9e+115)
		tmp = abs(((4.0 / y) + (x / y)));
	else
		tmp = abs((x / (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.6e+63], N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1.9e+115], N[Abs[N[(N[(4.0 / y), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 4: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+28}:\\ \;\;\;\;\left|x \cdot \left(\frac{z}{y} + \frac{-1}{y}\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e+28)
   (fabs (* x (+ (/ z y) (/ -1.0 y))))
   (fabs (/ (- (+ 4.0 x) (* x z)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+28) {
		tmp = fabs((x * ((z / y) + (-1.0 / y))));
	} else {
		tmp = fabs((((4.0 + x) - (x * z)) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1d+28)) then
        tmp = abs((x * ((z / y) + ((-1.0d0) / y))))
    else
        tmp = abs((((4.0d0 + x) - (x * z)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e+28) {
		tmp = Math.abs((x * ((z / y) + (-1.0 / y))));
	} else {
		tmp = Math.abs((((4.0 + x) - (x * z)) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e+28:
		tmp = math.fabs((x * ((z / y) + (-1.0 / y))))
	else:
		tmp = math.fabs((((4.0 + x) - (x * z)) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e+28)
		tmp = abs(Float64(x * Float64(Float64(z / y) + Float64(-1.0 / y))));
	else
		tmp = abs(Float64(Float64(Float64(4.0 + x) - Float64(x * z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e+28)
		tmp = abs((x * ((z / y) + (-1.0 / y))));
	else
		tmp = abs((((4.0 + x) - (x * z)) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e+28], N[Abs[N[(x * N[(N[(z / y), $MachinePrecision] + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(N[(4.0 + x), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]

Derivation

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

Alternative 5: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+63}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+112}:\\ \;\;\;\;\left|\frac{-4 - x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{\frac{y}{z}}\right|\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5e+63)
   (fabs (/ z (/ y x)))
   (if (<= z 1.15e+112) (fabs (/ (- -4.0 x) y)) (fabs (/ x (/ y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+63) {
		tmp = fabs((z / (y / x)));
	} else if (z <= 1.15e+112) {
		tmp = fabs(((-4.0 - x) / y));
	} else {
		tmp = fabs((x / (y / z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9.5d+63)) then
        tmp = abs((z / (y / x)))
    else if (z <= 1.15d+112) then
        tmp = abs((((-4.0d0) - x) / y))
    else
        tmp = abs((x / (y / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5e+63) {
		tmp = Math.abs((z / (y / x)));
	} else if (z <= 1.15e+112) {
		tmp = Math.abs(((-4.0 - x) / y));
	} else {
		tmp = Math.abs((x / (y / z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5e+63:
		tmp = math.fabs((z / (y / x)))
	elif z <= 1.15e+112:
		tmp = math.fabs(((-4.0 - x) / y))
	else:
		tmp = math.fabs((x / (y / z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5e+63)
		tmp = abs(Float64(z / Float64(y / x)));
	elseif (z <= 1.15e+112)
		tmp = abs(Float64(Float64(-4.0 - x) / y));
	else
		tmp = abs(Float64(x / Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5e+63)
		tmp = abs((z / (y / x)));
	elseif (z <= 1.15e+112)
		tmp = abs(((-4.0 - x) / y));
	else
		tmp = abs((x / (y / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5e+63], N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], If[LessEqual[z, 1.15e+112], N[Abs[N[(N[(-4.0 - x), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(x / N[(y / z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

Derivation

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

Alternative 6: 69.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 7: 41.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

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((4.0d0 / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]

Derivation

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

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))