Statistics.Sample:$swelfordMean from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 7

Speedup: 1.0×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - x) / 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 = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - x) / 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 = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - x) / 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 = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]

2. Final simplification 100.0%

   \[\leadsto x + \frac{y - x}{z} \]

Alternative 2: 57.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-209}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-233}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-210}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-117}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -3.15e+147)
     x
     (if (<= z -2.4e-209)
       (/ y z)
       (if (<= z -2.1e-233)
         t_0
         (if (<= z 8e-210)
           (/ y z)
           (if (<= z 2.35e-117) t_0 (if (<= z 2.15e+69) (/ y z) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= -2.4e-209) {
		tmp = y / z;
	} else if (z <= -2.1e-233) {
		tmp = t_0;
	} else if (z <= 8e-210) {
		tmp = y / z;
	} else if (z <= 2.35e-117) {
		tmp = t_0;
	} else if (z <= 2.15e+69) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	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) :: tmp
    t_0 = -x / z
    if (z <= (-3.15d+147)) then
        tmp = x
    else if (z <= (-2.4d-209)) then
        tmp = y / z
    else if (z <= (-2.1d-233)) then
        tmp = t_0
    else if (z <= 8d-210) then
        tmp = y / z
    else if (z <= 2.35d-117) then
        tmp = t_0
    else if (z <= 2.15d+69) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= -2.4e-209) {
		tmp = y / z;
	} else if (z <= -2.1e-233) {
		tmp = t_0;
	} else if (z <= 8e-210) {
		tmp = y / z;
	} else if (z <= 2.35e-117) {
		tmp = t_0;
	} else if (z <= 2.15e+69) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -3.15e+147:
		tmp = x
	elif z <= -2.4e-209:
		tmp = y / z
	elif z <= -2.1e-233:
		tmp = t_0
	elif z <= 8e-210:
		tmp = y / z
	elif z <= 2.35e-117:
		tmp = t_0
	elif z <= 2.15e+69:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= -2.4e-209)
		tmp = Float64(y / z);
	elseif (z <= -2.1e-233)
		tmp = t_0;
	elseif (z <= 8e-210)
		tmp = Float64(y / z);
	elseif (z <= 2.35e-117)
		tmp = t_0;
	elseif (z <= 2.15e+69)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= -2.4e-209)
		tmp = y / z;
	elseif (z <= -2.1e-233)
		tmp = t_0;
	elseif (z <= 8e-210)
		tmp = y / z;
	elseif (z <= 2.35e-117)
		tmp = t_0;
	elseif (z <= 2.15e+69)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -3.15e+147], x, If[LessEqual[z, -2.4e-209], N[(y / z), $MachinePrecision], If[LessEqual[z, -2.1e-233], t$95$0, If[LessEqual[z, 8e-210], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.35e-117], t$95$0, If[LessEqual[z, 2.15e+69], N[(y / z), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.14999999999999991e147 or 2.14999999999999996e69 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around inf 85.2%

      \[\leadsto \color{blue}{x} \]

   if -3.14999999999999991e147 < z < -2.4000000000000001e-209 or -2.0999999999999999e-233 < z < 8.0000000000000004e-210 or 2.35000000000000004e-117 < z < 2.14999999999999996e69

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around 0 60.6%

      \[\leadsto \color{blue}{\frac{y}{z}} \]

   if -2.4000000000000001e-209 < z < -2.0999999999999999e-233 or 8.0000000000000004e-210 < z < 2.35000000000000004e-117

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around 0 77.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{z}} \]
   4. Step-by-step derivation

      1. neg-mul-1 77.6%

         \[\leadsto \color{blue}{-\frac{x}{z}} \]

      2. distribute-neg-frac 77.6%

         \[\leadsto \color{blue}{\frac{-x}{z}} \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{-x}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-209}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-233}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-210}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-117}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0011:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{elif}\;z \leq 10^{+31}:\\ \;\;\;\;x + x \cdot \frac{-1}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.15e+147)
   x
   (if (<= z 0.0011)
     (/ (- y x) z)
     (if (<= z 1e+31) (+ x (* x (/ -1.0 z))) (if (<= z 2.2e+69) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= 0.0011) {
		tmp = (y - x) / z;
	} else if (z <= 1e+31) {
		tmp = x + (x * (-1.0 / z));
	} else if (z <= 2.2e+69) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	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 <= (-3.15d+147)) then
        tmp = x
    else if (z <= 0.0011d0) then
        tmp = (y - x) / z
    else if (z <= 1d+31) then
        tmp = x + (x * ((-1.0d0) / z))
    else if (z <= 2.2d+69) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= 0.0011) {
		tmp = (y - x) / z;
	} else if (z <= 1e+31) {
		tmp = x + (x * (-1.0 / z));
	} else if (z <= 2.2e+69) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.15e+147:
		tmp = x
	elif z <= 0.0011:
		tmp = (y - x) / z
	elif z <= 1e+31:
		tmp = x + (x * (-1.0 / z))
	elif z <= 2.2e+69:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= 0.0011)
		tmp = Float64(Float64(y - x) / z);
	elseif (z <= 1e+31)
		tmp = Float64(x + Float64(x * Float64(-1.0 / z)));
	elseif (z <= 2.2e+69)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= 0.0011)
		tmp = (y - x) / z;
	elseif (z <= 1e+31)
		tmp = x + (x * (-1.0 / z));
	elseif (z <= 2.2e+69)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.15e+147], x, If[LessEqual[z, 0.0011], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1e+31], N[(x + N[(x * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+69], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.14999999999999991e147 or 2.2000000000000002e69 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around inf 85.2%

      \[\leadsto \color{blue}{x} \]

   if -3.14999999999999991e147 < z < 0.00110000000000000007

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around 0 95.3%

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

   if 0.00110000000000000007 < z < 9.9999999999999996e30

   1. Initial program 99.8%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around inf 86.3%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{z}\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 86.3%

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

      2. sub-neg 86.3%

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

      3. distribute-rgt-in 86.3%

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

      4. *-lft-identity 86.3%

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

      5. distribute-neg-frac 86.3%

         \[\leadsto x + \color{blue}{\frac{-1}{z}} \cdot x \]

      6. metadata-eval 86.3%

         \[\leadsto x + \frac{\color{blue}{-1}}{z} \cdot x \]

   4. Simplified 86.3%

      \[\leadsto \color{blue}{x + \frac{-1}{z} \cdot x} \]

   if 9.9999999999999996e30 < z < 2.2000000000000002e69

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0011:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{elif}\;z \leq 10^{+31}:\\ \;\;\;\;x + x \cdot \frac{-1}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 81.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0012:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.15e+147)
   x
   (if (<= z 0.0012)
     (/ (- y x) z)
     (if (<= z 1.3e+31) (- x (/ x z)) (if (<= z 1.65e+71) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= 0.0012) {
		tmp = (y - x) / z;
	} else if (z <= 1.3e+31) {
		tmp = x - (x / z);
	} else if (z <= 1.65e+71) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	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 <= (-3.15d+147)) then
        tmp = x
    else if (z <= 0.0012d0) then
        tmp = (y - x) / z
    else if (z <= 1.3d+31) then
        tmp = x - (x / z)
    else if (z <= 1.65d+71) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= 0.0012) {
		tmp = (y - x) / z;
	} else if (z <= 1.3e+31) {
		tmp = x - (x / z);
	} else if (z <= 1.65e+71) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.15e+147:
		tmp = x
	elif z <= 0.0012:
		tmp = (y - x) / z
	elif z <= 1.3e+31:
		tmp = x - (x / z)
	elif z <= 1.65e+71:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= 0.0012)
		tmp = Float64(Float64(y - x) / z);
	elseif (z <= 1.3e+31)
		tmp = Float64(x - Float64(x / z));
	elseif (z <= 1.65e+71)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= 0.0012)
		tmp = (y - x) / z;
	elseif (z <= 1.3e+31)
		tmp = x - (x / z);
	elseif (z <= 1.65e+71)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.15e+147], x, If[LessEqual[z, 0.0012], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 1.3e+31], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.65e+71], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.14999999999999991e147 or 1.6499999999999999e71 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around inf 85.2%

      \[\leadsto \color{blue}{x} \]

   if -3.14999999999999991e147 < z < 0.00119999999999999989

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around 0 95.3%

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

   if 0.00119999999999999989 < z < 1.3e31

   1. Initial program 99.8%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in y around 0 86.0%

      \[\leadsto \color{blue}{x - \frac{x}{z}} \]

   if 1.3e31 < z < 1.6499999999999999e71

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around 0 79.4%

      \[\leadsto \color{blue}{\frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.0012:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.5e+89) (/ y z) (if (<= y 2.6e-17) (- x (/ x z)) (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+89) {
		tmp = y / z;
	} else if (y <= 2.6e-17) {
		tmp = x - (x / z);
	} else {
		tmp = 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 (y <= (-5.5d+89)) then
        tmp = y / z
    else if (y <= 2.6d-17) then
        tmp = x - (x / z)
    else
        tmp = y / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.5e+89) {
		tmp = y / z;
	} else if (y <= 2.6e-17) {
		tmp = x - (x / z);
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.5e+89:
		tmp = y / z
	elif y <= 2.6e-17:
		tmp = x - (x / z)
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.5e+89)
		tmp = Float64(y / z);
	elseif (y <= 2.6e-17)
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(y / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.5e+89)
		tmp = y / z;
	elseif (y <= 2.6e-17)
		tmp = x - (x / z);
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.5e+89], N[(y / z), $MachinePrecision], If[LessEqual[y, 2.6e-17], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999976e89 or 2.60000000000000003e-17 < y

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around 0 77.3%

      \[\leadsto \color{blue}{\frac{y}{z}} \]

   if -5.49999999999999976e89 < y < 2.60000000000000003e-17

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in y around 0 81.7%

      \[\leadsto \color{blue}{x - \frac{x}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-17}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \]

Alternative 6: 57.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.15e+147) x (if (<= z 2.15e+69) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= 2.15e+69) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	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 <= (-3.15d+147)) then
        tmp = x
    else if (z <= 2.15d+69) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.15e+147) {
		tmp = x;
	} else if (z <= 2.15e+69) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.15e+147:
		tmp = x
	elif z <= 2.15e+69:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= 2.15e+69)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.15e+147)
		tmp = x;
	elseif (z <= 2.15e+69)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.15e+147], x, If[LessEqual[z, 2.15e+69], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.14999999999999991e147 or 2.14999999999999996e69 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around inf 85.2%

      \[\leadsto \color{blue}{x} \]

   if -3.14999999999999991e147 < z < 2.14999999999999996e69

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around 0 55.1%

      \[\leadsto \color{blue}{\frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.15 \cdot 10^{+147}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 36.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]

2. Taylor expanded in z around inf 33.1%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 33.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))