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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 6

Speedup: 1.0×

• 20.7% 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: 61.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-99}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-192}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -0.68)
     x
     (if (<= z -1.1e-31)
       (/ y z)
       (if (<= z -4.2e-99)
         t_0
         (if (<= z -2.2e-171)
           (/ y z)
           (if (<= z 1.45e-229)
             t_0
             (if (<= z 1.6e-192) (/ y z) (if (<= z 2.95e-10) t_0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -0.68) {
		tmp = x;
	} else if (z <= -1.1e-31) {
		tmp = y / z;
	} else if (z <= -4.2e-99) {
		tmp = t_0;
	} else if (z <= -2.2e-171) {
		tmp = y / z;
	} else if (z <= 1.45e-229) {
		tmp = t_0;
	} else if (z <= 1.6e-192) {
		tmp = y / z;
	} else if (z <= 2.95e-10) {
		tmp = t_0;
	} 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 <= (-0.68d0)) then
        tmp = x
    else if (z <= (-1.1d-31)) then
        tmp = y / z
    else if (z <= (-4.2d-99)) then
        tmp = t_0
    else if (z <= (-2.2d-171)) then
        tmp = y / z
    else if (z <= 1.45d-229) then
        tmp = t_0
    else if (z <= 1.6d-192) then
        tmp = y / z
    else if (z <= 2.95d-10) then
        tmp = t_0
    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 <= -0.68) {
		tmp = x;
	} else if (z <= -1.1e-31) {
		tmp = y / z;
	} else if (z <= -4.2e-99) {
		tmp = t_0;
	} else if (z <= -2.2e-171) {
		tmp = y / z;
	} else if (z <= 1.45e-229) {
		tmp = t_0;
	} else if (z <= 1.6e-192) {
		tmp = y / z;
	} else if (z <= 2.95e-10) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -0.68:
		tmp = x
	elif z <= -1.1e-31:
		tmp = y / z
	elif z <= -4.2e-99:
		tmp = t_0
	elif z <= -2.2e-171:
		tmp = y / z
	elif z <= 1.45e-229:
		tmp = t_0
	elif z <= 1.6e-192:
		tmp = y / z
	elif z <= 2.95e-10:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -0.68)
		tmp = x;
	elseif (z <= -1.1e-31)
		tmp = Float64(y / z);
	elseif (z <= -4.2e-99)
		tmp = t_0;
	elseif (z <= -2.2e-171)
		tmp = Float64(y / z);
	elseif (z <= 1.45e-229)
		tmp = t_0;
	elseif (z <= 1.6e-192)
		tmp = Float64(y / z);
	elseif (z <= 2.95e-10)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -0.68)
		tmp = x;
	elseif (z <= -1.1e-31)
		tmp = y / z;
	elseif (z <= -4.2e-99)
		tmp = t_0;
	elseif (z <= -2.2e-171)
		tmp = y / z;
	elseif (z <= 1.45e-229)
		tmp = t_0;
	elseif (z <= 1.6e-192)
		tmp = y / z;
	elseif (z <= 2.95e-10)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -0.68], x, If[LessEqual[z, -1.1e-31], N[(y / z), $MachinePrecision], If[LessEqual[z, -4.2e-99], t$95$0, If[LessEqual[z, -2.2e-171], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.45e-229], t$95$0, If[LessEqual[z, 1.6e-192], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.95e-10], t$95$0, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.680000000000000049 or 2.9500000000000002e-10 < 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 inf 73.5%

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

   5. Taylor expanded in z around inf 69.9%

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

   if -0.680000000000000049 < z < -1.10000000000000005e-31 or -4.19999999999999968e-99 < z < -2.2000000000000001e-171 or 1.45e-229 < z < 1.6000000000000001e-192

   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 72.2%

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

      1. neg-mul-1 72.2%

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

      2. distribute-neg-frac 72.2%

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

   6. Simplified 72.2%

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

   7. Taylor expanded in x around 0 72.0%

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

   if -1.10000000000000005e-31 < z < -4.19999999999999968e-99 or -2.2000000000000001e-171 < z < 1.45e-229 or 1.6000000000000001e-192 < z < 2.9500000000000002e-10

   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 70.9%

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

   5. Taylor expanded in z around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. distribute-frac-neg 70.7%

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

   7. Simplified 70.7%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-99}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-171}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-229}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-192}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-10}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-191}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ (- x) z)))
   (if (<= z -2.9e-47)
     t_0
     (if (<= z -1.65e-98)
       t_1
       (if (<= z -1.8e-170)
         t_0
         (if (<= z 1.6e-229)
           t_1
           (if (<= z 1.05e-191) (/ y z) (if (<= z 1.8e-15) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double t_1 = -x / z;
	double tmp;
	if (z <= -2.9e-47) {
		tmp = t_0;
	} else if (z <= -1.65e-98) {
		tmp = t_1;
	} else if (z <= -1.8e-170) {
		tmp = t_0;
	} else if (z <= 1.6e-229) {
		tmp = t_1;
	} else if (z <= 1.05e-191) {
		tmp = y / z;
	} else if (z <= 1.8e-15) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y / z)
    t_1 = -x / z
    if (z <= (-2.9d-47)) then
        tmp = t_0
    else if (z <= (-1.65d-98)) then
        tmp = t_1
    else if (z <= (-1.8d-170)) then
        tmp = t_0
    else if (z <= 1.6d-229) then
        tmp = t_1
    else if (z <= 1.05d-191) then
        tmp = y / z
    else if (z <= 1.8d-15) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double t_1 = -x / z;
	double tmp;
	if (z <= -2.9e-47) {
		tmp = t_0;
	} else if (z <= -1.65e-98) {
		tmp = t_1;
	} else if (z <= -1.8e-170) {
		tmp = t_0;
	} else if (z <= 1.6e-229) {
		tmp = t_1;
	} else if (z <= 1.05e-191) {
		tmp = y / z;
	} else if (z <= 1.8e-15) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / z)
	t_1 = -x / z
	tmp = 0
	if z <= -2.9e-47:
		tmp = t_0
	elif z <= -1.65e-98:
		tmp = t_1
	elif z <= -1.8e-170:
		tmp = t_0
	elif z <= 1.6e-229:
		tmp = t_1
	elif z <= 1.05e-191:
		tmp = y / z
	elif z <= 1.8e-15:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y / z))
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -2.9e-47)
		tmp = t_0;
	elseif (z <= -1.65e-98)
		tmp = t_1;
	elseif (z <= -1.8e-170)
		tmp = t_0;
	elseif (z <= 1.6e-229)
		tmp = t_1;
	elseif (z <= 1.05e-191)
		tmp = Float64(y / z);
	elseif (z <= 1.8e-15)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y / z);
	t_1 = -x / z;
	tmp = 0.0;
	if (z <= -2.9e-47)
		tmp = t_0;
	elseif (z <= -1.65e-98)
		tmp = t_1;
	elseif (z <= -1.8e-170)
		tmp = t_0;
	elseif (z <= 1.6e-229)
		tmp = t_1;
	elseif (z <= 1.05e-191)
		tmp = y / z;
	elseif (z <= 1.8e-15)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -2.9e-47], t$95$0, If[LessEqual[z, -1.65e-98], t$95$1, If[LessEqual[z, -1.8e-170], t$95$0, If[LessEqual[z, 1.6e-229], t$95$1, If[LessEqual[z, 1.05e-191], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.8e-15], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e-47 or -1.6500000000000001e-98 < z < -1.8000000000000002e-170 or 1.8000000000000001e-15 < 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 92.0%

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

      1. neg-mul-1 92.0%

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

      2. distribute-neg-frac 92.0%

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

   6. Simplified 92.0%

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

      1. sub-neg 92.0%

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

      2. distribute-frac-neg 92.0%

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

      3. remove-double-neg 92.0%

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

      4. +-commutative 92.0%

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

   8. Applied egg-rr 92.0%

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

   if -2.9e-47 < z < -1.6500000000000001e-98 or -1.8000000000000002e-170 < z < 1.60000000000000007e-229 or 1.04999999999999993e-191 < z < 1.8000000000000001e-15

   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 71.6%

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

   5. Taylor expanded in z around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. distribute-frac-neg 71.6%

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

   7. Simplified 71.6%

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

   if 1.60000000000000007e-229 < z < 1.04999999999999993e-191

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. neg-sub0 99.9%

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

      3. neg-sub0 99.9%

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

      4. remove-double-neg 99.9%

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

      5. --rgt-identity 99.9%

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

      6. associate-+l- 99.9%

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

      7. div0 99.9%

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

      8. div-sub 99.9%

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

      9. associate-+l- 99.9%

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

      10. neg-sub0 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 67.1%

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

      1. neg-mul-1 67.1%

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

      2. distribute-neg-frac 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in x around 0 67.1%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-47}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-98}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-170}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-229}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-191}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 4: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-43} \lor \neg \left(x \leq 5.4 \cdot 10^{+26}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.1e-43) (not (<= x 5.4e+26))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.1e-43) || !(x <= 5.4e+26)) {
		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 <= (-1.1d-43)) .or. (.not. (x <= 5.4d+26))) 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 <= -1.1e-43) || !(x <= 5.4e+26)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.1e-43) or not (x <= 5.4e+26):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.1e-43) || !(x <= 5.4e+26))
		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 <= -1.1e-43) || ~((x <= 5.4e+26)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.1e-43], N[Not[LessEqual[x, 5.4e+26]], $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 < -1.09999999999999999e-43 or 5.4e26 < x

   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 88.7%

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

   if -1.09999999999999999e-43 < x < 5.4e26

   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 83.5%

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

      1. neg-mul-1 83.5%

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

      2. distribute-neg-frac 83.5%

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

   6. Simplified 83.5%

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

      1. sub-neg 83.5%

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

      2. distribute-frac-neg 83.5%

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

      3. remove-double-neg 83.5%

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

      4. +-commutative 83.5%

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

   8. Applied egg-rr 83.5%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-43} \lor \neg \left(x \leq 5.4 \cdot 10^{+26}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 5: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.68) x (if (<= z 2.2e+70) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.68) {
		tmp = x;
	} else if (z <= 2.2e+70) {
		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 <= (-0.68d0)) then
        tmp = x
    else if (z <= 2.2d+70) 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 <= -0.68) {
		tmp = x;
	} else if (z <= 2.2e+70) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.68:
		tmp = x
	elif z <= 2.2e+70:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.68)
		tmp = x;
	elseif (z <= 2.2e+70)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.68)
		tmp = x;
	elseif (z <= 2.2e+70)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.68], x, If[LessEqual[z, 2.2e+70], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -0.680000000000000049 or 2.20000000000000001e70 < 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 inf 78.7%

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

   5. Taylor expanded in z around inf 77.2%

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

   if -0.680000000000000049 < z < 2.20000000000000001e70

   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 52.2%

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

      1. neg-mul-1 52.2%

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

      2. distribute-neg-frac 52.2%

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

   6. Simplified 52.2%

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

   7. Taylor expanded in x around 0 46.3%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.68:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+70}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 36.6% 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 x around inf 66.7%

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

5. Taylor expanded in z around inf 33.6%

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

6. Final simplification 33.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023318 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))