fabs fraction 1

Percentage Accurate: 91.3% → 99.7%

Time: 9.9s

Alternatives: 9

Speedup: 1.0×

• 21.4% 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: 91.3% 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, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-45}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= y 5e-45)
   (fabs (/ (- (+ x 4.0) (* x z)) y))
   (fabs (- (/ (+ x 4.0) y) (* x (/ z y))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 5e-45) {
		tmp = fabs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = fabs((((x + 4.0) / y) - (x * (z / y))));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 (y <= 5d-45) then
        tmp = abs((((x + 4.0d0) - (x * z)) / y))
    else
        tmp = abs((((x + 4.0d0) / y) - (x * (z / y))))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5e-45) {
		tmp = Math.abs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = Math.abs((((x + 4.0) / y) - (x * (z / y))));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if y <= 5e-45:
		tmp = math.fabs((((x + 4.0) - (x * z)) / y))
	else:
		tmp = math.fabs((((x + 4.0) / y) - (x * (z / y))))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (y <= 5e-45)
		tmp = abs(Float64(Float64(Float64(x + 4.0) - Float64(x * z)) / y));
	else
		tmp = abs(Float64(Float64(Float64(x + 4.0) / y) - Float64(x * Float64(z / y))));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5e-45)
		tmp = abs((((x + 4.0) - (x * z)) / y));
	else
		tmp = abs((((x + 4.0) / y) - (x * (z / y))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[y, 5e-45], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision] - N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.99999999999999976e-45

   1. Initial program 94.9%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 94.4%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 89.8%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 89.8%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]
   4. Step-by-step derivation

      1. associate-*r/ 94.4%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. sub-div 97.3%

         \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   5. Applied egg-rr 97.3%

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   if 4.99999999999999976e-45 < y

   1. Initial program 98.6%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 94.9%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 99.9%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-45}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|\\ \end{array} \]

Alternative 2: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_0 := \left|z \cdot \frac{x}{y}\right|\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-124}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+96} \lor \neg \left(x \leq 4 \cdot 10^{+157}\right) \land x \leq 1.75 \cdot 10^{+204}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (* z (/ x y)))))
   (if (<= x -1.25e-124)
     t_0
     (if (<= x 4.0)
       (fabs (/ 4.0 y))
       (if (or (<= x 3.5e+96) (and (not (<= x 4e+157)) (<= x 1.75e+204)))
         (fabs (/ x y))
         t_0)))))

C

y = abs(y);
double code(double x, double y, double z) {
	double t_0 = fabs((z * (x / y)));
	double tmp;
	if (x <= -1.25e-124) {
		tmp = t_0;
	} else if (x <= 4.0) {
		tmp = fabs((4.0 / y));
	} else if ((x <= 3.5e+96) || (!(x <= 4e+157) && (x <= 1.75e+204))) {
		tmp = fabs((x / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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) :: tmp
    t_0 = abs((z * (x / y)))
    if (x <= (-1.25d-124)) then
        tmp = t_0
    else if (x <= 4.0d0) then
        tmp = abs((4.0d0 / y))
    else if ((x <= 3.5d+96) .or. (.not. (x <= 4d+157)) .and. (x <= 1.75d+204)) then
        tmp = abs((x / y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double t_0 = Math.abs((z * (x / y)));
	double tmp;
	if (x <= -1.25e-124) {
		tmp = t_0;
	} else if (x <= 4.0) {
		tmp = Math.abs((4.0 / y));
	} else if ((x <= 3.5e+96) || (!(x <= 4e+157) && (x <= 1.75e+204))) {
		tmp = Math.abs((x / y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	t_0 = math.fabs((z * (x / y)))
	tmp = 0
	if x <= -1.25e-124:
		tmp = t_0
	elif x <= 4.0:
		tmp = math.fabs((4.0 / y))
	elif (x <= 3.5e+96) or (not (x <= 4e+157) and (x <= 1.75e+204)):
		tmp = math.fabs((x / y))
	else:
		tmp = t_0
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	t_0 = abs(Float64(z * Float64(x / y)))
	tmp = 0.0
	if (x <= -1.25e-124)
		tmp = t_0;
	elseif (x <= 4.0)
		tmp = abs(Float64(4.0 / y));
	elseif ((x <= 3.5e+96) || (!(x <= 4e+157) && (x <= 1.75e+204)))
		tmp = abs(Float64(x / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	t_0 = abs((z * (x / y)));
	tmp = 0.0;
	if (x <= -1.25e-124)
		tmp = t_0;
	elseif (x <= 4.0)
		tmp = abs((4.0 / y));
	elseif ((x <= 3.5e+96) || (~((x <= 4e+157)) && (x <= 1.75e+204)))
		tmp = abs((x / y));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -1.25e-124], t$95$0, If[LessEqual[x, 4.0], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[x, 3.5e+96], And[N[Not[LessEqual[x, 4e+157]], $MachinePrecision], LessEqual[x, 1.75e+204]]], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2500000000000001e-124 or 3.4999999999999999e96 < x < 3.99999999999999993e157 or 1.74999999999999995e204 < x

   1. Initial program 94.1%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 91.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 93.6%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 93.6%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around inf 60.0%

      \[\leadsto \left|\color{blue}{-1 \cdot \frac{z \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. mul-1-neg 60.0%

         \[\leadsto \left|\color{blue}{-\frac{z \cdot x}{y}}\right| \]

      2. associate-/l* 69.3%

         \[\leadsto \left|-\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

      3. distribute-neg-frac 69.3%

         \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]

   6. Simplified 69.3%

      \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]
   7. Step-by-step derivation

      1. clear-num 69.2%

         \[\leadsto \left|\color{blue}{\frac{1}{\frac{\frac{y}{x}}{-z}}}\right| \]

      2. associate-/r/ 69.2%

         \[\leadsto \left|\color{blue}{\frac{1}{\frac{y}{x}} \cdot \left(-z\right)}\right| \]

      3. clear-num 69.2%

         \[\leadsto \left|\color{blue}{\frac{x}{y}} \cdot \left(-z\right)\right| \]

      4. add-sqr-sqrt 36.9%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right| \]

      5. sqrt-unprod 45.0%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right| \]

      6. sqr-neg 45.0%

         \[\leadsto \left|\frac{x}{y} \cdot \sqrt{\color{blue}{z \cdot z}}\right| \]

      7. sqrt-unprod 32.3%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right| \]

      8. add-sqr-sqrt 69.2%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{z}\right| \]

   8. Applied egg-rr 69.2%

      \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot z}\right| \]

   if -1.2500000000000001e-124 < x < 4

   1. Initial program 98.9%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 90.0%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in x around 0 82.1%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

   if 4 < x < 3.4999999999999999e96 or 3.99999999999999993e157 < x < 1.74999999999999995e204

   1. Initial program 94.6%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 92.5%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 97.3%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around 0 72.9%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-*r/ 72.9%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 72.9%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   6. Simplified 72.9%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]

   7. Taylor expanded in x around inf 68.9%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]
3. Recombined 3 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-124}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+96} \lor \neg \left(x \leq 4 \cdot 10^{+157}\right) \land x \leq 1.75 \cdot 10^{+204}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \end{array} \]

Alternative 3: 67.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} t_0 := \left|\frac{x}{y}\right|\\ t_1 := \left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{if}\;x \leq -1.25 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+98}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+208}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (fabs (/ x y))) (t_1 (fabs (/ z (/ y x)))))
   (if (<= x -1.25e-124)
     t_1
     (if (<= x 4.0)
       (fabs (/ 4.0 y))
       (if (<= x 7e+98)
         t_0
         (if (<= x 1.4e+160)
           t_1
           (if (<= x 3.4e+208) t_0 (fabs (* z (/ x y))))))))))

C

y = abs(y);
double code(double x, double y, double z) {
	double t_0 = fabs((x / y));
	double t_1 = fabs((z / (y / x)));
	double tmp;
	if (x <= -1.25e-124) {
		tmp = t_1;
	} else if (x <= 4.0) {
		tmp = fabs((4.0 / y));
	} else if (x <= 7e+98) {
		tmp = t_0;
	} else if (x <= 1.4e+160) {
		tmp = t_1;
	} else if (x <= 3.4e+208) {
		tmp = t_0;
	} else {
		tmp = fabs((z * (x / y)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 / (y / x)))
    if (x <= (-1.25d-124)) then
        tmp = t_1
    else if (x <= 4.0d0) then
        tmp = abs((4.0d0 / y))
    else if (x <= 7d+98) then
        tmp = t_0
    else if (x <= 1.4d+160) then
        tmp = t_1
    else if (x <= 3.4d+208) then
        tmp = t_0
    else
        tmp = abs((z * (x / y)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double t_0 = Math.abs((x / y));
	double t_1 = Math.abs((z / (y / x)));
	double tmp;
	if (x <= -1.25e-124) {
		tmp = t_1;
	} else if (x <= 4.0) {
		tmp = Math.abs((4.0 / y));
	} else if (x <= 7e+98) {
		tmp = t_0;
	} else if (x <= 1.4e+160) {
		tmp = t_1;
	} else if (x <= 3.4e+208) {
		tmp = t_0;
	} else {
		tmp = Math.abs((z * (x / y)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	t_0 = math.fabs((x / y))
	t_1 = math.fabs((z / (y / x)))
	tmp = 0
	if x <= -1.25e-124:
		tmp = t_1
	elif x <= 4.0:
		tmp = math.fabs((4.0 / y))
	elif x <= 7e+98:
		tmp = t_0
	elif x <= 1.4e+160:
		tmp = t_1
	elif x <= 3.4e+208:
		tmp = t_0
	else:
		tmp = math.fabs((z * (x / y)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	t_0 = abs(Float64(x / y))
	t_1 = abs(Float64(z / Float64(y / x)))
	tmp = 0.0
	if (x <= -1.25e-124)
		tmp = t_1;
	elseif (x <= 4.0)
		tmp = abs(Float64(4.0 / y));
	elseif (x <= 7e+98)
		tmp = t_0;
	elseif (x <= 1.4e+160)
		tmp = t_1;
	elseif (x <= 3.4e+208)
		tmp = t_0;
	else
		tmp = abs(Float64(z * Float64(x / y)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	t_0 = abs((x / y));
	t_1 = abs((z / (y / x)));
	tmp = 0.0;
	if (x <= -1.25e-124)
		tmp = t_1;
	elseif (x <= 4.0)
		tmp = abs((4.0 / y));
	elseif (x <= 7e+98)
		tmp = t_0;
	elseif (x <= 1.4e+160)
		tmp = t_1;
	elseif (x <= 3.4e+208)
		tmp = t_0;
	else
		tmp = abs((z * (x / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := Block[{t$95$0 = N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, -1.25e-124], t$95$1, If[LessEqual[x, 4.0], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 7e+98], t$95$0, If[LessEqual[x, 1.4e+160], t$95$1, If[LessEqual[x, 3.4e+208], t$95$0, N[Abs[N[(z * N[(x / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.2500000000000001e-124 or 7e98 < x < 1.4e160

   1. Initial program 96.0%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 92.4%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 94.3%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 94.3%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around inf 59.2%

      \[\leadsto \left|\color{blue}{-1 \cdot \frac{z \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. mul-1-neg 59.2%

         \[\leadsto \left|\color{blue}{-\frac{z \cdot x}{y}}\right| \]

      2. associate-/l* 67.5%

         \[\leadsto \left|-\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

      3. distribute-neg-frac 67.5%

         \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]

   6. Simplified 67.5%

      \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]
   7. Step-by-step derivation

      1. associate-/r/ 61.1%

         \[\leadsto \left|\color{blue}{\frac{-z}{y} \cdot x}\right| \]

      2. add-sqr-sqrt 33.1%

         \[\leadsto \left|\frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}{y} \cdot x\right| \]

      3. sqrt-unprod 41.7%

         \[\leadsto \left|\frac{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}{y} \cdot x\right| \]

      4. sqr-neg 41.7%

         \[\leadsto \left|\frac{\sqrt{\color{blue}{z \cdot z}}}{y} \cdot x\right| \]

      5. sqrt-unprod 27.7%

         \[\leadsto \left|\frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{y} \cdot x\right| \]

      6. add-sqr-sqrt 61.1%

         \[\leadsto \left|\frac{\color{blue}{z}}{y} \cdot x\right| \]

   8. Applied egg-rr 61.1%

      \[\leadsto \left|\color{blue}{\frac{z}{y} \cdot x}\right| \]
   9. Step-by-step derivation

      1. associate-*l/ 59.2%

         \[\leadsto \left|\color{blue}{\frac{z \cdot x}{y}}\right| \]

      2. associate-/l* 67.5%

         \[\leadsto \left|\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

   10. Applied egg-rr 67.5%

       \[\leadsto \left|\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

   if -1.2500000000000001e-124 < x < 4

   1. Initial program 98.9%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 90.0%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in x around 0 82.1%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

   if 4 < x < 7e98 or 1.4e160 < x < 3.3999999999999998e208

   1. Initial program 94.6%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 92.5%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 97.3%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 97.3%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around 0 72.9%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-*r/ 72.9%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 72.9%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   6. Simplified 72.9%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]

   7. Taylor expanded in x around inf 68.9%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

   if 3.3999999999999998e208 < x

   1. Initial program 84.1%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 84.5%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 89.5%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 89.5%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around inf 64.2%

      \[\leadsto \left|\color{blue}{-1 \cdot \frac{z \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. mul-1-neg 64.2%

         \[\leadsto \left|\color{blue}{-\frac{z \cdot x}{y}}\right| \]

      2. associate-/l* 79.1%

         \[\leadsto \left|-\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

      3. distribute-neg-frac 79.1%

         \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]

   6. Simplified 79.1%

      \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]
   7. Step-by-step derivation

      1. clear-num 79.0%

         \[\leadsto \left|\color{blue}{\frac{1}{\frac{\frac{y}{x}}{-z}}}\right| \]

      2. associate-/r/ 79.1%

         \[\leadsto \left|\color{blue}{\frac{1}{\frac{y}{x}} \cdot \left(-z\right)}\right| \]

      3. clear-num 79.1%

         \[\leadsto \left|\color{blue}{\frac{x}{y}} \cdot \left(-z\right)\right| \]

      4. add-sqr-sqrt 32.1%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right| \]

      5. sqrt-unprod 63.5%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right| \]

      6. sqr-neg 63.5%

         \[\leadsto \left|\frac{x}{y} \cdot \sqrt{\color{blue}{z \cdot z}}\right| \]

      7. sqrt-unprod 47.0%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right| \]

      8. add-sqr-sqrt 79.1%

         \[\leadsto \left|\frac{x}{y} \cdot \color{blue}{z}\right| \]

   8. Applied egg-rr 79.1%

      \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot z}\right| \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-124}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;x \leq 4:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+98}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+160}:\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+208}:\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|z \cdot \frac{x}{y}\right|\\ \end{array} \]

Alternative 4: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-15} \lor \neg \left(z \leq 800000\right):\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.46e-15) (not (<= z 800000.0)))
   (fabs (* (/ x y) (- 1.0 z)))
   (fabs (/ (+ x 4.0) y))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.46e-15) || !(z <= 800000.0)) {
		tmp = fabs(((x / y) * (1.0 - z)));
	} else {
		tmp = fabs(((x + 4.0) / y));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-1.46d-15)) .or. (.not. (z <= 800000.0d0))) then
        tmp = abs(((x / y) * (1.0d0 - z)))
    else
        tmp = abs(((x + 4.0d0) / y))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.46e-15) || !(z <= 800000.0)) {
		tmp = Math.abs(((x / y) * (1.0 - z)));
	} else {
		tmp = Math.abs(((x + 4.0) / y));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if (z <= -1.46e-15) or not (z <= 800000.0):
		tmp = math.fabs(((x / y) * (1.0 - z)))
	else:
		tmp = math.fabs(((x + 4.0) / y))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.46e-15) || !(z <= 800000.0))
		tmp = abs(Float64(Float64(x / y) * Float64(1.0 - z)));
	else
		tmp = abs(Float64(Float64(x + 4.0) / y));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.46e-15) || ~((z <= 800000.0)))
		tmp = abs(((x / y) * (1.0 - z)));
	else
		tmp = abs(((x + 4.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[Or[LessEqual[z, -1.46e-15], N[Not[LessEqual[z, 800000.0]], $MachinePrecision]], N[Abs[N[(N[(x / y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4600000000000001e-15 or 8e5 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 76.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y}} - \frac{x}{y} \cdot z\right| \]
   3. Step-by-step derivation

      1. *-un-lft-identity 76.4%

         \[\leadsto \left|\color{blue}{1 \cdot \frac{x}{y}} - \frac{x}{y} \cdot z\right| \]

      2. *-commutative 76.4%

         \[\leadsto \left|1 \cdot \frac{x}{y} - \color{blue}{z \cdot \frac{x}{y}}\right| \]

      3. distribute-rgt-out-- 79.4%

         \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot \left(1 - z\right)}\right| \]

   4. Applied egg-rr 79.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot \left(1 - z\right)}\right| \]

   if -1.4600000000000001e-15 < z < 8e5

   1. Initial program 96.7%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 99.1%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 99.1%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around 0 100.0%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   5. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto \left|\color{blue}{\frac{x}{y} + 4 \cdot \frac{1}{y}}\right| \]

      2. *-rgt-identity 100.0%

         \[\leadsto \left|\frac{\color{blue}{x \cdot 1}}{y} + 4 \cdot \frac{1}{y}\right| \]

      3. associate-*r/ 99.8%

         \[\leadsto \left|\color{blue}{x \cdot \frac{1}{y}} + 4 \cdot \frac{1}{y}\right| \]

      4. distribute-rgt-in 99.8%

         \[\leadsto \left|\color{blue}{\frac{1}{y} \cdot \left(x + 4\right)}\right| \]

      5. associate-*l/ 100.0%

         \[\leadsto \left|\color{blue}{\frac{1 \cdot \left(x + 4\right)}{y}}\right| \]

      6. *-lft-identity 100.0%

         \[\leadsto \left|\frac{\color{blue}{x + 4}}{y}\right| \]

   6. Simplified 100.0%

      \[\leadsto \left|\color{blue}{\frac{x + 4}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-15} \lor \neg \left(z \leq 800000\right):\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y}\right|\\ \end{array} \]

Alternative 5: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-15} \lor \neg \left(z \leq 108000000000\right):\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} + \frac{4}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.46e-15) (not (<= z 108000000000.0)))
   (fabs (* (/ x y) (- 1.0 z)))
   (fabs (+ (/ x y) (/ 4.0 y)))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.46e-15) || !(z <= 108000000000.0)) {
		tmp = fabs(((x / y) * (1.0 - z)));
	} else {
		tmp = fabs(((x / y) + (4.0 / y)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-1.46d-15)) .or. (.not. (z <= 108000000000.0d0))) then
        tmp = abs(((x / y) * (1.0d0 - z)))
    else
        tmp = abs(((x / y) + (4.0d0 / y)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.46e-15) || !(z <= 108000000000.0)) {
		tmp = Math.abs(((x / y) * (1.0 - z)));
	} else {
		tmp = Math.abs(((x / y) + (4.0 / y)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if (z <= -1.46e-15) or not (z <= 108000000000.0):
		tmp = math.fabs(((x / y) * (1.0 - z)))
	else:
		tmp = math.fabs(((x / y) + (4.0 / y)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.46e-15) || !(z <= 108000000000.0))
		tmp = abs(Float64(Float64(x / y) * Float64(1.0 - z)));
	else
		tmp = abs(Float64(Float64(x / y) + Float64(4.0 / y)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.46e-15) || ~((z <= 108000000000.0)))
		tmp = abs(((x / y) * (1.0 - z)));
	else
		tmp = abs(((x / y) + (4.0 / y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[Or[LessEqual[z, -1.46e-15], N[Not[LessEqual[z, 108000000000.0]], $MachinePrecision]], N[Abs[N[(N[(x / y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x / y), $MachinePrecision] + N[(4.0 / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4600000000000001e-15 or 1.08e11 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 76.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y}} - \frac{x}{y} \cdot z\right| \]
   3. Step-by-step derivation

      1. *-un-lft-identity 76.4%

         \[\leadsto \left|\color{blue}{1 \cdot \frac{x}{y}} - \frac{x}{y} \cdot z\right| \]

      2. *-commutative 76.4%

         \[\leadsto \left|1 \cdot \frac{x}{y} - \color{blue}{z \cdot \frac{x}{y}}\right| \]

      3. distribute-rgt-out-- 79.4%

         \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot \left(1 - z\right)}\right| \]

   4. Applied egg-rr 79.4%

      \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot \left(1 - z\right)}\right| \]

   if -1.4600000000000001e-15 < z < 1.08e11

   1. Initial program 96.7%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 99.1%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 99.1%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around 0 100.0%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 100.0%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   6. Simplified 100.0%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.46 \cdot 10^{-15} \lor \neg \left(z \leq 108000000000\right):\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} + \frac{4}{y}\right|\\ \end{array} \]

Alternative 6: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 3.7 \cdot 10^{+147}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (<= x 3.7e+147)
   (fabs (/ (- (+ x 4.0) (* x z)) y))
   (fabs (* (/ x y) (- 1.0 z)))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.7e+147) {
		tmp = fabs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = fabs(((x / y) * (1.0 - z)));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= 3.7d+147) then
        tmp = abs((((x + 4.0d0) - (x * z)) / y))
    else
        tmp = abs(((x / y) * (1.0d0 - z)))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 3.7e+147) {
		tmp = Math.abs((((x + 4.0) - (x * z)) / y));
	} else {
		tmp = Math.abs(((x / y) * (1.0 - z)));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if x <= 3.7e+147:
		tmp = math.fabs((((x + 4.0) - (x * z)) / y))
	else:
		tmp = math.fabs(((x / y) * (1.0 - z)))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if (x <= 3.7e+147)
		tmp = abs(Float64(Float64(Float64(x + 4.0) - Float64(x * z)) / y));
	else
		tmp = abs(Float64(Float64(x / y) * Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 3.7e+147)
		tmp = abs((((x + 4.0) - (x * z)) / y));
	else
		tmp = abs(((x / y) * (1.0 - z)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[LessEqual[x, 3.7e+147], N[Abs[N[(N[(N[(x + 4.0), $MachinePrecision] - N[(x * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x / y), $MachinePrecision] * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.7e147

   1. Initial program 97.6%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 97.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 93.0%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]
   4. Step-by-step derivation

      1. associate-*r/ 97.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. sub-div 98.1%

         \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   5. Applied egg-rr 98.1%

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right| \]

   if 3.7e147 < x

   1. Initial program 86.1%

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

   2. Taylor expanded in x around inf 86.1%

      \[\leadsto \left|\color{blue}{\frac{x}{y}} - \frac{x}{y} \cdot z\right| \]
   3. Step-by-step derivation

      1. *-un-lft-identity 86.1%

         \[\leadsto \left|\color{blue}{1 \cdot \frac{x}{y}} - \frac{x}{y} \cdot z\right| \]

      2. *-commutative 86.1%

         \[\leadsto \left|1 \cdot \frac{x}{y} - \color{blue}{z \cdot \frac{x}{y}}\right| \]

      3. distribute-rgt-out-- 100.0%

         \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot \left(1 - z\right)}\right| \]

   4. Applied egg-rr 100.0%

      \[\leadsto \left|\color{blue}{\frac{x}{y} \cdot \left(1 - z\right)}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.7 \cdot 10^{+147}:\\ \;\;\;\;\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(1 - z\right)\right|\\ \end{array} \]

Alternative 7: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -44000 \lor \neg \left(z \leq 7200000000000\right):\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -44000.0) (not (<= z 7200000000000.0)))
   (fabs (/ z (/ y x)))
   (fabs (/ (+ x 4.0) y))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -44000.0) || !(z <= 7200000000000.0)) {
		tmp = fabs((z / (y / x)));
	} else {
		tmp = fabs(((x + 4.0) / y));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-44000.0d0)) .or. (.not. (z <= 7200000000000.0d0))) then
        tmp = abs((z / (y / x)))
    else
        tmp = abs(((x + 4.0d0) / y))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -44000.0) || !(z <= 7200000000000.0)) {
		tmp = Math.abs((z / (y / x)));
	} else {
		tmp = Math.abs(((x + 4.0) / y));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if (z <= -44000.0) or not (z <= 7200000000000.0):
		tmp = math.fabs((z / (y / x)))
	else:
		tmp = math.fabs(((x + 4.0) / y))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if ((z <= -44000.0) || !(z <= 7200000000000.0))
		tmp = abs(Float64(z / Float64(y / x)));
	else
		tmp = abs(Float64(Float64(x + 4.0) / y));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -44000.0) || ~((z <= 7200000000000.0)))
		tmp = abs((z / (y / x)));
	else
		tmp = abs(((x + 4.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[Or[LessEqual[z, -44000.0], N[Not[LessEqual[z, 7200000000000.0]], $MachinePrecision]], N[Abs[N[(z / N[(y / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(x + 4.0), $MachinePrecision] / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -44000 or 7.2e12 < z

   1. Initial program 95.2%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 90.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 86.7%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around inf 73.9%

      \[\leadsto \left|\color{blue}{-1 \cdot \frac{z \cdot x}{y}}\right| \]
   5. Step-by-step derivation

      1. mul-1-neg 73.9%

         \[\leadsto \left|\color{blue}{-\frac{z \cdot x}{y}}\right| \]

      2. associate-/l* 78.9%

         \[\leadsto \left|-\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

      3. distribute-neg-frac 78.9%

         \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]

   6. Simplified 78.9%

      \[\leadsto \left|\color{blue}{\frac{-z}{\frac{y}{x}}}\right| \]
   7. Step-by-step derivation

      1. associate-/r/ 74.5%

         \[\leadsto \left|\color{blue}{\frac{-z}{y} \cdot x}\right| \]

      2. add-sqr-sqrt 39.3%

         \[\leadsto \left|\frac{\color{blue}{\sqrt{-z} \cdot \sqrt{-z}}}{y} \cdot x\right| \]

      3. sqrt-unprod 51.8%

         \[\leadsto \left|\frac{\color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}}{y} \cdot x\right| \]

      4. sqr-neg 51.8%

         \[\leadsto \left|\frac{\sqrt{\color{blue}{z \cdot z}}}{y} \cdot x\right| \]

      5. sqrt-unprod 35.0%

         \[\leadsto \left|\frac{\color{blue}{\sqrt{z} \cdot \sqrt{z}}}{y} \cdot x\right| \]

      6. add-sqr-sqrt 74.5%

         \[\leadsto \left|\frac{\color{blue}{z}}{y} \cdot x\right| \]

   8. Applied egg-rr 74.5%

      \[\leadsto \left|\color{blue}{\frac{z}{y} \cdot x}\right| \]
   9. Step-by-step derivation

      1. associate-*l/ 73.9%

         \[\leadsto \left|\color{blue}{\frac{z \cdot x}{y}}\right| \]

      2. associate-/l* 78.9%

         \[\leadsto \left|\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

   10. Applied egg-rr 78.9%

       \[\leadsto \left|\color{blue}{\frac{z}{\frac{y}{x}}}\right| \]

   if -44000 < z < 7.2e12

   1. Initial program 96.8%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 99.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 99.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 99.2%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around 0 99.2%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   5. Step-by-step derivation

      1. +-commutative 99.2%

         \[\leadsto \left|\color{blue}{\frac{x}{y} + 4 \cdot \frac{1}{y}}\right| \]

      2. *-rgt-identity 99.2%

         \[\leadsto \left|\frac{\color{blue}{x \cdot 1}}{y} + 4 \cdot \frac{1}{y}\right| \]

      3. associate-*r/ 99.0%

         \[\leadsto \left|\color{blue}{x \cdot \frac{1}{y}} + 4 \cdot \frac{1}{y}\right| \]

      4. distribute-rgt-in 99.0%

         \[\leadsto \left|\color{blue}{\frac{1}{y} \cdot \left(x + 4\right)}\right| \]

      5. associate-*l/ 99.2%

         \[\leadsto \left|\color{blue}{\frac{1 \cdot \left(x + 4\right)}{y}}\right| \]

      6. *-lft-identity 99.2%

         \[\leadsto \left|\frac{\color{blue}{x + 4}}{y}\right| \]

   6. Simplified 99.2%

      \[\leadsto \left|\color{blue}{\frac{x + 4}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -44000 \lor \neg \left(z \leq 7200000000000\right):\\ \;\;\;\;\left|\frac{z}{\frac{y}{x}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{x + 4}{y}\right|\\ \end{array} \]

Alternative 8: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} y = |y|\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \end{array} \]

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55) (not (<= x 4.0))) (fabs (/ x y)) (fabs (/ 4.0 y))))

C

y = abs(y);
double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55) || !(x <= 4.0)) {
		tmp = fabs((x / y));
	} else {
		tmp = fabs((4.0 / y));
	}
	return tmp;
}

Fortran

NOTE: y should be positive before calling this function
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 <= (-1.55d0)) .or. (.not. (x <= 4.0d0))) then
        tmp = abs((x / y))
    else
        tmp = abs((4.0d0 / y))
    end if
    code = tmp
end function

Java

y = Math.abs(y);
public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55) || !(x <= 4.0)) {
		tmp = Math.abs((x / y));
	} else {
		tmp = Math.abs((4.0 / y));
	}
	return tmp;
}

Python

y = abs(y)
def code(x, y, z):
	tmp = 0
	if (x <= -1.55) or not (x <= 4.0):
		tmp = math.fabs((x / y))
	else:
		tmp = math.fabs((4.0 / y))
	return tmp

Julia

y = abs(y)
function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55) || !(x <= 4.0))
		tmp = abs(Float64(x / y));
	else
		tmp = abs(Float64(4.0 / y));
	end
	return tmp
end

MATLAB

y = abs(y)
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.55) || ~((x <= 4.0)))
		tmp = abs((x / y));
	else
		tmp = abs((4.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := If[Or[LessEqual[x, -1.55], N[Not[LessEqual[x, 4.0]], $MachinePrecision]], N[Abs[N[(x / y), $MachinePrecision]], $MachinePrecision], N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000004 or 4 < x

   1. Initial program 93.8%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 89.7%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 96.1%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 96.1%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in z around 0 56.9%

      \[\leadsto \left|\color{blue}{4 \cdot \frac{1}{y} + \frac{x}{y}}\right| \]
   5. Step-by-step derivation

      1. associate-*r/ 56.9%

         \[\leadsto \left|\color{blue}{\frac{4 \cdot 1}{y}} + \frac{x}{y}\right| \]

      2. metadata-eval 56.9%

         \[\leadsto \left|\frac{\color{blue}{4}}{y} + \frac{x}{y}\right| \]

   6. Simplified 56.9%

      \[\leadsto \left|\color{blue}{\frac{4}{y} + \frac{x}{y}}\right| \]

   7. Taylor expanded in x around inf 55.2%

      \[\leadsto \left|\color{blue}{\frac{x}{y}}\right| \]

   if -1.55000000000000004 < x < 4

   1. Initial program 98.3%

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
   2. Step-by-step derivation

      1. associate-*l/ 99.8%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

      2. associate-*r/ 89.2%

         \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

   3. Simplified 89.2%

      \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

   4. Taylor expanded in x around 0 72.8%

      \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \lor \neg \left(x \leq 4\right):\\ \;\;\;\;\left|\frac{x}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4}{y}\right|\\ \end{array} \]

Alternative 9: 40.6% accurate, 1.1× speedup

Math

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

FPCore

NOTE: y should be positive before calling this function
(FPCore (x y z) :precision binary64 (fabs (/ 4.0 y)))

C

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

Fortran

NOTE: y should be positive before calling this function
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

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: y should be positive before calling this function
code[x_, y_, z_] := N[Abs[N[(4.0 / y), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 96.0%

   \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \]
2. Step-by-step derivation

   1. associate-*l/ 94.6%

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right| \]

   2. associate-*r/ 92.8%

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \frac{z}{y}}\right| \]

3. Simplified 92.8%

   \[\leadsto \color{blue}{\left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right|} \]

4. Taylor expanded in x around 0 37.7%

   \[\leadsto \left|\color{blue}{\frac{4}{y}}\right| \]

5. Final simplification 37.7%

   \[\leadsto \left|\frac{4}{y}\right| \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "fabs fraction 1"
  :precision binary64
  (fabs (- (/ (+ x 4.0) y) (* (/ x y) z))))