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

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 7

Speedup: 1.0×

• 20.5% 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: 61.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{-z}\\ \mathbf{if}\;z \leq -620000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-240}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-293}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-170}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z))))
   (if (<= z -620000000.0)
     x
     (if (<= z -7.2e-240)
       (/ y z)
       (if (<= z 5.6e-293)
         t_0
         (if (<= z 8e-170) (/ y z) (if (<= z 1.0) t_0 x)))))))

C

double code(double x, double y, double z) {
	double t_0 = x / -z;
	double tmp;
	if (z <= -620000000.0) {
		tmp = x;
	} else if (z <= -7.2e-240) {
		tmp = y / z;
	} else if (z <= 5.6e-293) {
		tmp = t_0;
	} else if (z <= 8e-170) {
		tmp = y / z;
	} else if (z <= 1.0) {
		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 <= (-620000000.0d0)) then
        tmp = x
    else if (z <= (-7.2d-240)) then
        tmp = y / z
    else if (z <= 5.6d-293) then
        tmp = t_0
    else if (z <= 8d-170) then
        tmp = y / z
    else if (z <= 1.0d0) 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 <= -620000000.0) {
		tmp = x;
	} else if (z <= -7.2e-240) {
		tmp = y / z;
	} else if (z <= 5.6e-293) {
		tmp = t_0;
	} else if (z <= 8e-170) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / -z
	tmp = 0
	if z <= -620000000.0:
		tmp = x
	elif z <= -7.2e-240:
		tmp = y / z
	elif z <= 5.6e-293:
		tmp = t_0
	elif z <= 8e-170:
		tmp = y / z
	elif z <= 1.0:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(-z))
	tmp = 0.0
	if (z <= -620000000.0)
		tmp = x;
	elseif (z <= -7.2e-240)
		tmp = Float64(y / z);
	elseif (z <= 5.6e-293)
		tmp = t_0;
	elseif (z <= 8e-170)
		tmp = Float64(y / z);
	elseif (z <= 1.0)
		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 <= -620000000.0)
		tmp = x;
	elseif (z <= -7.2e-240)
		tmp = y / z;
	elseif (z <= 5.6e-293)
		tmp = t_0;
	elseif (z <= 8e-170)
		tmp = y / z;
	elseif (z <= 1.0)
		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, -620000000.0], x, If[LessEqual[z, -7.2e-240], N[(y / z), $MachinePrecision], If[LessEqual[z, 5.6e-293], t$95$0, If[LessEqual[z, 8e-170], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$0, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e8 or 1 < 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. sub-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r- 100.0%

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

      9. 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 73.0%

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

   if -6.2e8 < z < -7.1999999999999998e-240 or 5.60000000000000051e-293 < z < 7.99999999999999987e-170

   1. Initial program 99.9%

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

      1. div-sub 97.8%

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

      2. sub-neg 97.8%

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

      3. distribute-frac-neg 97.8%

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

      4. +-commutative 97.8%

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

      5. associate-+r+ 97.8%

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

      6. distribute-frac-neg 97.8%

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

      7. sub-neg 97.8%

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

      8. associate--r- 97.8%

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

      9. div-sub 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 62.5%

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

   if -7.1999999999999998e-240 < z < 5.60000000000000051e-293 or 7.99999999999999987e-170 < z < 1

   1. Initial program 100.0%

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

      1. div-sub 92.2%

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

      2. sub-neg 92.2%

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

      3. distribute-frac-neg 92.2%

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

      4. +-commutative 92.2%

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

      5. associate-+r+ 92.2%

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

      6. distribute-frac-neg 92.2%

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

      7. sub-neg 92.2%

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

      8. associate--r- 92.2%

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

      9. 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 71.7%

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

   6. Taylor expanded in z around 0 68.8%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

   8. Simplified 68.8%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -620000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-240}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-293}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-170}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{x}{-z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-239}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-294}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-169}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.045:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ x (- z))))
   (if (<= z -1.35e-239)
     t_0
     (if (<= z 2.4e-294)
       t_1
       (if (<= z 1.15e-169) (/ y z) (if (<= z 0.045) 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 <= -1.35e-239) {
		tmp = t_0;
	} else if (z <= 2.4e-294) {
		tmp = t_1;
	} else if (z <= 1.15e-169) {
		tmp = y / z;
	} else if (z <= 0.045) {
		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 <= (-1.35d-239)) then
        tmp = t_0
    else if (z <= 2.4d-294) then
        tmp = t_1
    else if (z <= 1.15d-169) then
        tmp = y / z
    else if (z <= 0.045d0) 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 <= -1.35e-239) {
		tmp = t_0;
	} else if (z <= 2.4e-294) {
		tmp = t_1;
	} else if (z <= 1.15e-169) {
		tmp = y / z;
	} else if (z <= 0.045) {
		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 <= -1.35e-239:
		tmp = t_0
	elif z <= 2.4e-294:
		tmp = t_1
	elif z <= 1.15e-169:
		tmp = y / z
	elif z <= 0.045:
		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(x / Float64(-z))
	tmp = 0.0
	if (z <= -1.35e-239)
		tmp = t_0;
	elseif (z <= 2.4e-294)
		tmp = t_1;
	elseif (z <= 1.15e-169)
		tmp = Float64(y / z);
	elseif (z <= 0.045)
		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 <= -1.35e-239)
		tmp = t_0;
	elseif (z <= 2.4e-294)
		tmp = t_1;
	elseif (z <= 1.15e-169)
		tmp = y / z;
	elseif (z <= 0.045)
		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, -1.35e-239], t$95$0, If[LessEqual[z, 2.4e-294], t$95$1, If[LessEqual[z, 1.15e-169], N[(y / z), $MachinePrecision], If[LessEqual[z, 0.045], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e-239 or 0.044999999999999998 < z

   1. Initial program 100.0%

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

      1. div-sub 99.4%

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

      2. sub-neg 99.4%

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

      3. distribute-frac-neg 99.4%

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

      4. +-commutative 99.4%

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

      5. associate-+r+ 99.4%

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

      6. distribute-frac-neg 99.4%

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

      7. sub-neg 99.4%

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

      8. associate--r- 99.4%

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

      9. 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 84.3%

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

      1. neg-mul-1 84.3%

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

      2. distribute-neg-frac2 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in x around 0 84.3%

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

      1. sub-neg 84.3%

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

      2. mul-1-neg 84.3%

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

      3. remove-double-neg 84.3%

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

      4. +-commutative 84.3%

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

   10. Simplified 84.3%

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

   if -1.35e-239 < z < 2.39999999999999997e-294 or 1.15e-169 < z < 0.044999999999999998

   1. Initial program 100.0%

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

      1. div-sub 92.2%

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

      2. sub-neg 92.2%

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

      3. distribute-frac-neg 92.2%

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

      4. +-commutative 92.2%

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

      5. associate-+r+ 92.2%

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

      6. distribute-frac-neg 92.2%

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

      7. sub-neg 92.2%

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

      8. associate--r- 92.2%

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

      9. 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 71.7%

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

   6. Taylor expanded in z around 0 68.8%

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

      1. associate-*r/ 68.8%

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

      2. neg-mul-1 68.8%

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

   8. Simplified 68.8%

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

   if 2.39999999999999997e-294 < z < 1.15e-169

   1. Initial program 99.9%

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

      1. div-sub 96.7%

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

      2. sub-neg 96.7%

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

      3. distribute-frac-neg 96.7%

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

      4. +-commutative 96.7%

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

      5. associate-+r+ 96.7%

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

      6. distribute-frac-neg 96.7%

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

      7. sub-neg 96.7%

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

      8. associate--r- 96.7%

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

      9. div-sub 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 77.3%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-239}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-169}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.045:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+18} \lor \neg \left(y \leq 10^{+79}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.9e+18) (not (<= y 1e+79))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.9e+18) || !(y <= 1e+79)) {
		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 <= (-6.9d+18)) .or. (.not. (y <= 1d+79))) 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 <= -6.9e+18) || !(y <= 1e+79)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.9e+18) or not (y <= 1e+79):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.9e+18) || !(y <= 1e+79))
		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 <= -6.9e+18) || ~((y <= 1e+79)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.9e+18], N[Not[LessEqual[y, 1e+79]], $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 < -6.9e18 or 9.99999999999999967e78 < y

   1. Initial program 100.0%

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

      1. div-sub 94.3%

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

      2. sub-neg 94.3%

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

      3. distribute-frac-neg 94.3%

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

      4. +-commutative 94.3%

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

      5. associate-+r+ 94.3%

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

      6. distribute-frac-neg 94.3%

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

      7. sub-neg 94.3%

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

      8. associate--r- 94.3%

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

      9. 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 94.0%

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

      1. neg-mul-1 94.0%

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

      2. distribute-neg-frac2 94.0%

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

   7. Simplified 94.0%

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

   8. Taylor expanded in x around 0 94.0%

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

      1. sub-neg 94.0%

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

      2. mul-1-neg 94.0%

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

      3. remove-double-neg 94.0%

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

      4. +-commutative 94.0%

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

   10. Simplified 94.0%

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

   if -6.9e18 < y < 9.99999999999999967e78

   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. sub-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r- 100.0%

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

      9. 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 86.3%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.9 \cdot 10^{+18} \lor \neg \left(y \leq 10^{+79}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $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 1 < 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. sub-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r- 100.0%

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

      9. 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 98.0%

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

      1. neg-mul-1 98.0%

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

      2. distribute-neg-frac2 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in x around 0 98.0%

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

      1. sub-neg 98.0%

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

      2. mul-1-neg 98.0%

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

      3. remove-double-neg 98.0%

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

      4. +-commutative 98.0%

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

   10. Simplified 98.0%

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

   if -1 < z < 1

   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. sub-neg 95.7%

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

      3. distribute-frac-neg 95.7%

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

      4. +-commutative 95.7%

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

      5. associate-+r+ 95.7%

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

      6. distribute-frac-neg 95.7%

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

      7. sub-neg 95.7%

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

      8. associate--r- 95.7%

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

      9. 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 98.9%

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

4. Final simplification 98.5%

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

Alternative 6: 62.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -650000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -650000000.0) x (if (<= z 1.6e+28) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -650000000.0) {
		tmp = x;
	} else if (z <= 1.6e+28) {
		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 <= (-650000000.0d0)) then
        tmp = x
    else if (z <= 1.6d+28) 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 <= -650000000.0) {
		tmp = x;
	} else if (z <= 1.6e+28) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -650000000.0:
		tmp = x
	elif z <= 1.6e+28:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -650000000.0)
		tmp = x;
	elseif (z <= 1.6e+28)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -650000000.0)
		tmp = x;
	elseif (z <= 1.6e+28)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -650000000.0], x, If[LessEqual[z, 1.6e+28], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e8 or 1.6e28 < 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. sub-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r- 100.0%

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

      9. 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 75.9%

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

   if -6.5e8 < z < 1.6e28

   1. Initial program 100.0%

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

      1. div-sub 96.0%

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

      2. sub-neg 96.0%

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

      3. distribute-frac-neg 96.0%

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

      4. +-commutative 96.0%

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

      5. associate-+r+ 96.0%

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

      6. distribute-frac-neg 96.0%

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

      7. sub-neg 96.0%

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

      8. associate--r- 96.0%

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

      9. 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 51.6%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -650000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+28}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 37.1% 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 97.6%

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

   2. sub-neg 97.6%

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

   3. distribute-frac-neg 97.6%

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

   4. +-commutative 97.6%

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

   5. associate-+r+ 97.6%

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

   6. distribute-frac-neg 97.6%

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

   7. sub-neg 97.6%

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

   8. associate--r- 97.6%

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

   9. 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 33.8%

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

6. Final simplification 33.8%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))