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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 7

Speedup: 1.0×

• 21.1% 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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \frac{y - x}{z} \]
4. Add Preprocessing

Alternative 2: 61.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-242}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-211}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.1e+34)
     x
     (if (<= z -4.4e-242)
       (/ y z)
       (if (<= z 2.2e-211)
         t_0
         (if (<= z 2.8e-56)
           (/ y z)
           (if (<= z 2.3e-26) t_0 (if (<= z 8.8e+21) (/ y z) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.1e+34) {
		tmp = x;
	} else if (z <= -4.4e-242) {
		tmp = y / z;
	} else if (z <= 2.2e-211) {
		tmp = t_0;
	} else if (z <= 2.8e-56) {
		tmp = y / z;
	} else if (z <= 2.3e-26) {
		tmp = t_0;
	} else if (z <= 8.8e+21) {
		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 <= (-1.1d+34)) then
        tmp = x
    else if (z <= (-4.4d-242)) then
        tmp = y / z
    else if (z <= 2.2d-211) then
        tmp = t_0
    else if (z <= 2.8d-56) then
        tmp = y / z
    else if (z <= 2.3d-26) then
        tmp = t_0
    else if (z <= 8.8d+21) 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 <= -1.1e+34) {
		tmp = x;
	} else if (z <= -4.4e-242) {
		tmp = y / z;
	} else if (z <= 2.2e-211) {
		tmp = t_0;
	} else if (z <= 2.8e-56) {
		tmp = y / z;
	} else if (z <= 2.3e-26) {
		tmp = t_0;
	} else if (z <= 8.8e+21) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.1e+34:
		tmp = x
	elif z <= -4.4e-242:
		tmp = y / z
	elif z <= 2.2e-211:
		tmp = t_0
	elif z <= 2.8e-56:
		tmp = y / z
	elif z <= 2.3e-26:
		tmp = t_0
	elif z <= 8.8e+21:
		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 <= -1.1e+34)
		tmp = x;
	elseif (z <= -4.4e-242)
		tmp = Float64(y / z);
	elseif (z <= 2.2e-211)
		tmp = t_0;
	elseif (z <= 2.8e-56)
		tmp = Float64(y / z);
	elseif (z <= 2.3e-26)
		tmp = t_0;
	elseif (z <= 8.8e+21)
		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 <= -1.1e+34)
		tmp = x;
	elseif (z <= -4.4e-242)
		tmp = y / z;
	elseif (z <= 2.2e-211)
		tmp = t_0;
	elseif (z <= 2.8e-56)
		tmp = y / z;
	elseif (z <= 2.3e-26)
		tmp = t_0;
	elseif (z <= 8.8e+21)
		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, -1.1e+34], x, If[LessEqual[z, -4.4e-242], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.2e-211], t$95$0, If[LessEqual[z, 2.8e-56], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.3e-26], t$95$0, If[LessEqual[z, 8.8e+21], N[(y / z), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1000000000000001e34 or 8.8e21 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 80.0%

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

   if -1.1000000000000001e34 < z < -4.40000000000000003e-242 or 2.19999999999999998e-211 < z < 2.79999999999999993e-56 or 2.30000000000000009e-26 < z < 8.8e21

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 95.2%

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

      2. associate-+r- 95.2%

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

      3. remove-double-neg 95.2%

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

      4. distribute-frac-neg 95.2%

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

      5. unsub-neg 95.2%

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

      6. associate--r+ 95.2%

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

      7. +-commutative 95.2%

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

      8. distribute-frac-neg 95.2%

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

      9. sub-neg 95.2%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 63.7%

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

   if -4.40000000000000003e-242 < z < 2.19999999999999998e-211 or 2.79999999999999993e-56 < z < 2.30000000000000009e-26

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 86.0%

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

      2. associate-+r- 86.0%

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

      3. remove-double-neg 86.0%

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

      4. distribute-frac-neg 86.0%

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

      5. unsub-neg 86.0%

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

      6. associate--r+ 86.0%

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

      7. +-commutative 86.0%

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

      8. distribute-frac-neg 86.0%

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

      9. sub-neg 86.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.5%

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

   6. Taylor expanded in z around 0 76.5%

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

      1. mul-1-neg 76.5%

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

      2. distribute-frac-neg 76.5%

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

   8. Simplified 76.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-242}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-211}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-26}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+245} \lor \neg \left(x \leq 6.5 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4e+245) (not (<= x 6.5e+211))) (/ (- x) z) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+245) || !(x <= 6.5e+211)) {
		tmp = -x / z;
	} else {
		tmp = 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 ((x <= (-4d+245)) .or. (.not. (x <= 6.5d+211))) then
        tmp = -x / z
    else
        tmp = x + (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4e+245) || !(x <= 6.5e+211)) {
		tmp = -x / z;
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4e+245) or not (x <= 6.5e+211):
		tmp = -x / z
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4e+245) || !(x <= 6.5e+211))
		tmp = Float64(Float64(-x) / z);
	else
		tmp = Float64(x + Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4e+245) || ~((x <= 6.5e+211)))
		tmp = -x / z;
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4e+245], N[Not[LessEqual[x, 6.5e+211]], $MachinePrecision]], N[((-x) / z), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000018e245 or 6.4999999999999996e211 < x

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 82.5%

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

      2. associate-+r- 82.5%

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

      3. remove-double-neg 82.5%

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

      4. distribute-frac-neg 82.5%

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

      5. unsub-neg 82.5%

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

      6. associate--r+ 82.5%

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

      7. +-commutative 82.5%

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

      8. distribute-frac-neg 82.5%

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

      9. sub-neg 82.5%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 95.0%

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

   6. Taylor expanded in z around 0 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-frac-neg 70.8%

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

   8. Simplified 70.8%

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

   if -4.00000000000000018e245 < x < 6.4999999999999996e211

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 98.1%

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

      2. associate-+r- 98.1%

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

      3. remove-double-neg 98.1%

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

      4. distribute-frac-neg 98.1%

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

      5. unsub-neg 98.1%

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

      6. associate--r+ 98.1%

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

      7. +-commutative 98.1%

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

      8. distribute-frac-neg 98.1%

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

      9. sub-neg 98.1%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 80.2%

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

      1. neg-mul-1 80.2%

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

      2. distribute-neg-frac 80.2%

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

   7. Simplified 80.2%

      \[\leadsto x - \color{blue}{\frac{-y}{z}} \]
   8. Step-by-step derivation

      1. sub-neg 80.2%

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

      2. distribute-frac-neg 80.2%

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

      3. remove-double-neg 80.2%

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

      4. +-commutative 80.2%

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

   9. Applied egg-rr 80.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+245} \lor \neg \left(x \leq 6.5 \cdot 10^{+211}\right):\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+117} \lor \neg \left(x \leq 0.0032\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.2e+117) (not (<= x 0.0032))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+117) || !(x <= 0.0032)) {
		tmp = x - (x / z);
	} else {
		tmp = 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 ((x <= (-6.2d+117)) .or. (.not. (x <= 0.0032d0))) then
        tmp = x - (x / z)
    else
        tmp = x + (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.2e+117) || !(x <= 0.0032)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.2e+117) or not (x <= 0.0032):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.2e+117) || !(x <= 0.0032))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(x + Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.2e+117) || ~((x <= 0.0032)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.2e+117], N[Not[LessEqual[x, 0.0032]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999995e117 or 0.00320000000000000015 < x

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 90.3%

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

      2. associate-+r- 90.3%

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

      3. remove-double-neg 90.3%

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

      4. distribute-frac-neg 90.3%

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

      5. unsub-neg 90.3%

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

      6. associate--r+ 90.3%

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

      7. +-commutative 90.3%

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

      8. distribute-frac-neg 90.3%

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

      9. sub-neg 90.3%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 90.1%

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

   if -6.1999999999999995e117 < x < 0.00320000000000000015

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 88.4%

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

      1. neg-mul-1 88.4%

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

      2. distribute-neg-frac 88.4%

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

   7. Simplified 88.4%

      \[\leadsto x - \color{blue}{\frac{-y}{z}} \]
   8. Step-by-step derivation

      1. sub-neg 88.4%

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

      2. distribute-frac-neg 88.4%

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

      3. remove-double-neg 88.4%

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

      4. +-commutative 88.4%

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

   9. Applied egg-rr 88.4%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+117} \lor \neg \left(x \leq 0.0032\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2.15 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 2.15e-5))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 2.15e-5)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / 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 <= (-1.0d0)) .or. (.not. (z <= 2.15d-5))) then
        tmp = x + (y / z)
    else
        tmp = (y - x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 2.15e-5)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 2.15e-5):
		tmp = x + (y / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 2.15e-5))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(Float64(y - x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 2.15e-5)))
		tmp = x + (y / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 2.15e-5]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 2.1500000000000001e-5 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 98.3%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac 98.3%

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

   7. Simplified 98.3%

      \[\leadsto x - \color{blue}{\frac{-y}{z}} \]
   8. Step-by-step derivation

      1. sub-neg 98.3%

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

      2. distribute-frac-neg 98.3%

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

      3. remove-double-neg 98.3%

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

      4. +-commutative 98.3%

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

   9. Applied egg-rr 98.3%

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

   if -1 < z < 2.1500000000000001e-5

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 92.0%

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

      2. associate-+r- 92.0%

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

      3. remove-double-neg 92.0%

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

      4. distribute-frac-neg 92.0%

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

      5. unsub-neg 92.0%

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

      6. associate--r+ 92.0%

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

      7. +-commutative 92.0%

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

      8. distribute-frac-neg 92.0%

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

      9. sub-neg 92.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 100.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 2.15 \cdot 10^{-5}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.5e+33) x (if (<= z 8.5e+24) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.5e+33) {
		tmp = x;
	} else if (z <= 8.5e+24) {
		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 <= (-8.5d+33)) then
        tmp = x
    else if (z <= 8.5d+24) 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 <= -8.5e+33) {
		tmp = x;
	} else if (z <= 8.5e+24) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.5e+33:
		tmp = x
	elif z <= 8.5e+24:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.5e+33)
		tmp = x;
	elseif (z <= 8.5e+24)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.5e+33)
		tmp = x;
	elseif (z <= 8.5e+24)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.5e+33], x, If[LessEqual[z, 8.5e+24], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.4999999999999998e33 or 8.49999999999999959e24 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 80.0%

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

   if -8.4999999999999998e33 < z < 8.49999999999999959e24

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Step-by-step derivation

      1. div-sub 92.6%

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

      2. associate-+r- 92.6%

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

      3. remove-double-neg 92.6%

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

      4. distribute-frac-neg 92.6%

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

      5. unsub-neg 92.6%

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

      6. associate--r+ 92.6%

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

      7. +-commutative 92.6%

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

      8. distribute-frac-neg 92.6%

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

      9. sub-neg 92.6%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 53.6%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+33}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.2% 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. Step-by-step derivation

   1. div-sub 95.7%

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

   2. associate-+r- 95.7%

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

   3. remove-double-neg 95.7%

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

   4. distribute-frac-neg 95.7%

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

   5. unsub-neg 95.7%

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

   6. associate--r+ 95.7%

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

   7. +-commutative 95.7%

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

   8. distribute-frac-neg 95.7%

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

   9. sub-neg 95.7%

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

   10. div-sub 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 36.1%

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

6. Final simplification 36.1%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))