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

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 7

Speedup: 1.0×

• 20.6% 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: 61.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.45e+38)
   x
   (if (<= z -6.6e-144)
     (/ y z)
     (if (<= z 1.05e-222) (/ (- x) z) (if (<= z 6.1e+38) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e+38) {
		tmp = x;
	} else if (z <= -6.6e-144) {
		tmp = y / z;
	} else if (z <= 1.05e-222) {
		tmp = -x / z;
	} else if (z <= 6.1e+38) {
		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 <= (-2.45d+38)) then
        tmp = x
    else if (z <= (-6.6d-144)) then
        tmp = y / z
    else if (z <= 1.05d-222) then
        tmp = -x / z
    else if (z <= 6.1d+38) 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 <= -2.45e+38) {
		tmp = x;
	} else if (z <= -6.6e-144) {
		tmp = y / z;
	} else if (z <= 1.05e-222) {
		tmp = -x / z;
	} else if (z <= 6.1e+38) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.45e+38:
		tmp = x
	elif z <= -6.6e-144:
		tmp = y / z
	elif z <= 1.05e-222:
		tmp = -x / z
	elif z <= 6.1e+38:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.45e+38)
		tmp = x;
	elseif (z <= -6.6e-144)
		tmp = Float64(y / z);
	elseif (z <= 1.05e-222)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 6.1e+38)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.45e+38)
		tmp = x;
	elseif (z <= -6.6e-144)
		tmp = y / z;
	elseif (z <= 1.05e-222)
		tmp = -x / z;
	elseif (z <= 6.1e+38)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.45e+38], x, If[LessEqual[z, -6.6e-144], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.05e-222], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 6.1e+38], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000001e38 or 6.0999999999999999e38 < z

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 76.4%

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

   if -2.45000000000000001e38 < z < -6.5999999999999999e-144 or 1.05e-222 < z < 6.0999999999999999e38

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 65.0%

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

   if -6.5999999999999999e-144 < z < 1.05e-222

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 72.7%

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

      1. distribute-lft-out-- 72.7%

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

      2. *-rgt-identity 72.7%

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

      3. associate-*r/ 72.9%

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

      4. *-rgt-identity 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in z around 0 72.9%

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

      1. neg-mul-1 72.9%

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

      2. distribute-neg-frac 72.9%

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

   9. Simplified 72.9%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-144}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-144} \lor \neg \left(z \leq 7 \cdot 10^{-224}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e-144) (not (<= z 7e-224))) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-144) || !(z <= 7e-224)) {
		tmp = x + (y / z);
	} else {
		tmp = -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 <= (-4.4d-144)) .or. (.not. (z <= 7d-224))) then
        tmp = x + (y / z)
    else
        tmp = -x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-144) || !(z <= 7e-224)) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e-144) or not (z <= 7e-224):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e-144) || !(z <= 7e-224))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.4e-144) || ~((z <= 7e-224)))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e-144], N[Not[LessEqual[z, 7e-224]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000012e-144 or 7.00000000000000037e-224 < z

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 87.9%

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

      1. neg-mul-1 87.9%

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

      2. distribute-neg-frac 87.9%

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

   6. Simplified 87.9%

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

   7. Taylor expanded in x around 0 87.9%

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

      1. +-commutative 87.9%

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

   9. Simplified 87.9%

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

   if -4.40000000000000012e-144 < z < 7.00000000000000037e-224

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 72.7%

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

      1. distribute-lft-out-- 72.7%

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

      2. *-rgt-identity 72.7%

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

      3. associate-*r/ 72.9%

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

      4. *-rgt-identity 72.9%

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

   6. Simplified 72.9%

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

   7. Taylor expanded in z around 0 72.9%

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

      1. neg-mul-1 72.9%

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

      2. distribute-neg-frac 72.9%

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

   9. Simplified 72.9%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-144} \lor \neg \left(z \leq 7 \cdot 10^{-224}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 4: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-123} \lor \neg \left(y \leq 1.9 \cdot 10^{-57}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e-123) (not (<= y 1.9e-57))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e-123) || !(y <= 1.9e-57)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (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 ((y <= (-2.8d-123)) .or. (.not. (y <= 1.9d-57))) then
        tmp = x + (y / z)
    else
        tmp = x - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e-123) || !(y <= 1.9e-57)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e-123) or not (y <= 1.9e-57):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e-123) || !(y <= 1.9e-57))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(x - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.8e-123) || ~((y <= 1.9e-57)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e-123], N[Not[LessEqual[y, 1.9e-57]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7999999999999999e-123 or 1.8999999999999999e-57 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 89.2%

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

      1. neg-mul-1 89.2%

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

      2. distribute-neg-frac 89.2%

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

   6. Simplified 89.2%

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

   7. Taylor expanded in x around 0 89.2%

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

      1. +-commutative 89.2%

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

   9. Simplified 89.2%

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

   if -2.7999999999999999e-123 < y < 1.8999999999999999e-57

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 88.6%

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

      1. distribute-lft-out-- 88.6%

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

      2. *-rgt-identity 88.6%

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

      3. associate-*r/ 88.7%

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

      4. *-rgt-identity 88.7%

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

   6. Simplified 88.7%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-123} \lor \neg \left(y \leq 1.9 \cdot 10^{-57}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 5: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3600 \lor \neg \left(z \leq 2.5 \cdot 10^{-30}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3600.0) (not (<= z 2.5e-30))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3600.0) || !(z <= 2.5e-30)) {
		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 <= (-3600.0d0)) .or. (.not. (z <= 2.5d-30))) 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 <= -3600.0) || !(z <= 2.5e-30)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3600.0) or not (z <= 2.5e-30):
		tmp = x + (y / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3600.0) || !(z <= 2.5e-30))
		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 <= -3600.0) || ~((z <= 2.5e-30)))
		tmp = x + (y / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3600.0], N[Not[LessEqual[z, 2.5e-30]], $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 < -3600 or 2.49999999999999986e-30 < z

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 98.7%

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

      1. neg-mul-1 98.7%

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

      2. distribute-neg-frac 98.7%

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

   6. Simplified 98.7%

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

   7. Taylor expanded in x around 0 98.7%

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

      1. +-commutative 98.7%

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

   9. Simplified 98.7%

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

   if -3600 < z < 2.49999999999999986e-30

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 99.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3600 \lor \neg \left(z \leq 2.5 \cdot 10^{-30}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 6: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.5e+32) x (if (<= z 6.1e+25) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.5e+32) {
		tmp = x;
	} else if (z <= 6.1e+25) {
		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 <= (-6.5d+32)) then
        tmp = x
    else if (z <= 6.1d+25) 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 <= -6.5e+32) {
		tmp = x;
	} else if (z <= 6.1e+25) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.5e+32:
		tmp = x
	elif z <= 6.1e+25:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.5e+32)
		tmp = x;
	elseif (z <= 6.1e+25)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.5e+32)
		tmp = x;
	elseif (z <= 6.1e+25)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.5e+32], x, If[LessEqual[z, 6.1e+25], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4999999999999994e32 or 6.1000000000000003e25 < z

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 76.4%

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

   if -6.4999999999999994e32 < z < 6.1000000000000003e25

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 55.0%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 36.8% 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. remove-double-neg 100.0%

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

   2. neg-sub0 100.0%

      \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

   3. neg-sub0 100.0%

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

   4. remove-double-neg 100.0%

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

   5. --rgt-identity 100.0%

      \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

   6. associate-+l- 100.0%

      \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

   7. div0 100.0%

      \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

   8. div-sub 100.0%

      \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

   9. associate-+l- 100.0%

      \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

   10. neg-sub0 100.0%

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

   11. +-commutative 100.0%

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

   12. sub-neg 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in z around inf 39.3%

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

5. Final simplification 39.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023336 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))