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

Percentage Accurate: 100.0% → 100.0%

Time: 6.4s

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. Add Preprocessing

Alternative 2: 59.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-143}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 10^{+34} \lor \neg \left(z \leq 1.5 \cdot 10^{+135}\right) \land z \leq 5.5 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+14)
   x
   (if (<= z -4.2e-63)
     (/ y z)
     (if (<= z 8e-143)
       (/ (- x) z)
       (if (or (<= z 1e+34) (and (not (<= z 1.5e+135)) (<= z 5.5e+184)))
         (/ y z)
         x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+14) {
		tmp = x;
	} else if (z <= -4.2e-63) {
		tmp = y / z;
	} else if (z <= 8e-143) {
		tmp = -x / z;
	} else if ((z <= 1e+34) || (!(z <= 1.5e+135) && (z <= 5.5e+184))) {
		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 <= (-9d+14)) then
        tmp = x
    else if (z <= (-4.2d-63)) then
        tmp = y / z
    else if (z <= 8d-143) then
        tmp = -x / z
    else if ((z <= 1d+34) .or. (.not. (z <= 1.5d+135)) .and. (z <= 5.5d+184)) 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 <= -9e+14) {
		tmp = x;
	} else if (z <= -4.2e-63) {
		tmp = y / z;
	} else if (z <= 8e-143) {
		tmp = -x / z;
	} else if ((z <= 1e+34) || (!(z <= 1.5e+135) && (z <= 5.5e+184))) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+14:
		tmp = x
	elif z <= -4.2e-63:
		tmp = y / z
	elif z <= 8e-143:
		tmp = -x / z
	elif (z <= 1e+34) or (not (z <= 1.5e+135) and (z <= 5.5e+184)):
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+14)
		tmp = x;
	elseif (z <= -4.2e-63)
		tmp = Float64(y / z);
	elseif (z <= 8e-143)
		tmp = Float64(Float64(-x) / z);
	elseif ((z <= 1e+34) || (!(z <= 1.5e+135) && (z <= 5.5e+184)))
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+14)
		tmp = x;
	elseif (z <= -4.2e-63)
		tmp = y / z;
	elseif (z <= 8e-143)
		tmp = -x / z;
	elseif ((z <= 1e+34) || (~((z <= 1.5e+135)) && (z <= 5.5e+184)))
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+14], x, If[LessEqual[z, -4.2e-63], N[(y / z), $MachinePrecision], If[LessEqual[z, 8e-143], N[((-x) / z), $MachinePrecision], If[Or[LessEqual[z, 1e+34], And[N[Not[LessEqual[z, 1.5e+135]], $MachinePrecision], LessEqual[z, 5.5e+184]]], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9e14 or 9.99999999999999946e33 < z < 1.5e135 or 5.5000000000000002e184 < 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 82.2%

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

   if -9e14 < z < -4.2e-63 or 7.9999999999999996e-143 < z < 9.99999999999999946e33 or 1.5e135 < z < 5.5000000000000002e184

   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 71.8%

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

   if -4.2e-63 < z < 7.9999999999999996e-143

   1. Initial program 100.0%

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

      1. div-sub 91.2%

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

      2. sub-neg 91.2%

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

      3. distribute-frac-neg 91.2%

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

      4. +-commutative 91.2%

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

      5. associate-+r+ 91.2%

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

      6. distribute-frac-neg 91.2%

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

      7. sub-neg 91.2%

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

      8. associate--r- 91.2%

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

      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 62.4%

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

      1. distribute-lft-out-- 62.4%

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

      2. *-rgt-identity 62.4%

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

      3. associate-*r/ 62.5%

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

      4. *-rgt-identity 62.5%

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

   7. Simplified 62.5%

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

   8. Taylor expanded in z around 0 62.5%

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

      1. mul-1-neg 62.5%

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

      2. distribute-frac-neg 62.5%

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

   10. Simplified 62.5%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-143}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 10^{+34} \lor \neg \left(z \leq 1.5 \cdot 10^{+135}\right) \land z \leq 5.5 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+26} \lor \neg \left(z \leq 1.6 \cdot 10^{+133}\right) \land z \leq 1.75 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.95e+15)
   x
   (if (or (<= z 7.8e+26) (and (not (<= z 1.6e+133)) (<= z 1.75e+184)))
     (/ y z)
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.95e+15) {
		tmp = x;
	} else if ((z <= 7.8e+26) || (!(z <= 1.6e+133) && (z <= 1.75e+184))) {
		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 <= (-1.95d+15)) then
        tmp = x
    else if ((z <= 7.8d+26) .or. (.not. (z <= 1.6d+133)) .and. (z <= 1.75d+184)) 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 <= -1.95e+15) {
		tmp = x;
	} else if ((z <= 7.8e+26) || (!(z <= 1.6e+133) && (z <= 1.75e+184))) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.95e+15:
		tmp = x
	elif (z <= 7.8e+26) or (not (z <= 1.6e+133) and (z <= 1.75e+184)):
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.95e+15)
		tmp = x;
	elseif ((z <= 7.8e+26) || (!(z <= 1.6e+133) && (z <= 1.75e+184)))
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.95e+15)
		tmp = x;
	elseif ((z <= 7.8e+26) || (~((z <= 1.6e+133)) && (z <= 1.75e+184)))
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.95e+15], x, If[Or[LessEqual[z, 7.8e+26], And[N[Not[LessEqual[z, 1.6e+133]], $MachinePrecision], LessEqual[z, 1.75e+184]]], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.95e15 or 7.8e26 < z < 1.59999999999999999e133 or 1.74999999999999989e184 < 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 82.2%

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

   if -1.95e15 < z < 7.8e26 or 1.59999999999999999e133 < z < 1.74999999999999989e184

   1. Initial program 100.0%

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

      1. div-sub 94.8%

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

      2. sub-neg 94.8%

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

      3. distribute-frac-neg 94.8%

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

      4. +-commutative 94.8%

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

      5. associate-+r+ 94.8%

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

      6. distribute-frac-neg 94.8%

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

      7. sub-neg 94.8%

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

      8. associate--r- 94.8%

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

      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 56.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+26} \lor \neg \left(z \leq 1.6 \cdot 10^{+133}\right) \land z \leq 1.75 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -6.2e+14) (not (<= z 1.0))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -6.2e+14) || !(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 <= (-6.2d+14)) .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 <= -6.2e+14) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -6.2e+14) 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 <= -6.2e+14) || !(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 <= -6.2e+14) || ~((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, -6.2e+14], 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 < -6.2e14 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 99.6%

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

      1. neg-mul-1 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0 99.6%

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

      1. cancel-sign-sub-inv 99.6%

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

      2. metadata-eval 99.6%

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

      3. *-lft-identity 99.6%

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

      4. +-commutative 99.6%

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

   10. Simplified 99.6%

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

   if -6.2e14 < z < 1

   1. Initial program 100.0%

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

      1. div-sub 94.1%

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

      2. sub-neg 94.1%

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

      3. distribute-frac-neg 94.1%

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

      4. +-commutative 94.1%

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

      5. associate-+r+ 94.1%

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

      6. distribute-frac-neg 94.1%

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

      7. sub-neg 94.1%

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

      8. associate--r- 94.1%

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

      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 99.4%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+14} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+92} \lor \neg \left(y \leq 0.01\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+92) (not (<= y 0.01))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+92) || !(y <= 0.01)) {
		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 <= (-1d+92)) .or. (.not. (y <= 0.01d0))) 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 <= -1e+92) || !(y <= 0.01)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+92) or not (y <= 0.01):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+92) || !(y <= 0.01))
		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 <= -1e+92) || ~((y <= 0.01)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+92], N[Not[LessEqual[y, 0.01]], $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 < -1e92 or 0.0100000000000000002 < y

   1. Initial program 100.0%

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

      1. div-sub 95.0%

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

      2. sub-neg 95.0%

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

      3. distribute-frac-neg 95.0%

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

      4. +-commutative 95.0%

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

      5. associate-+r+ 95.0%

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

      6. distribute-frac-neg 95.0%

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

      7. sub-neg 95.0%

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

      8. associate--r- 95.0%

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

      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 94.1%

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

      1. neg-mul-1 94.1%

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

   7. Simplified 94.1%

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

   8. Taylor expanded in x around 0 94.1%

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

      1. cancel-sign-sub-inv 94.1%

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

      2. metadata-eval 94.1%

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

      3. *-lft-identity 94.1%

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

      4. +-commutative 94.1%

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

   10. Simplified 94.1%

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

   if -1e92 < y < 0.0100000000000000002

   1. Initial program 100.0%

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

      1. div-sub 98.5%

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

      2. sub-neg 98.5%

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

      3. distribute-frac-neg 98.5%

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

      4. +-commutative 98.5%

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

      5. associate-+r+ 98.5%

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

      6. distribute-frac-neg 98.5%

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

      7. sub-neg 98.5%

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

      8. associate--r- 98.5%

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

      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 83.8%

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

      1. distribute-lft-out-- 83.8%

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

      2. *-rgt-identity 83.8%

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

      3. associate-*r/ 83.8%

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

      4. *-rgt-identity 83.8%

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

   7. Simplified 83.8%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+92} \lor \neg \left(y \leq 0.01\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-131} \lor \neg \left(z \leq 4.7 \cdot 10^{-150}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.3e-131) (not (<= z 4.7e-150))) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.3e-131) || !(z <= 4.7e-150)) {
		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 <= (-4.3d-131)) .or. (.not. (z <= 4.7d-150))) 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 <= -4.3e-131) || !(z <= 4.7e-150)) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.3e-131) or not (z <= 4.7e-150):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.3e-131) || !(z <= 4.7e-150))
		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 <= -4.3e-131) || ~((z <= 4.7e-150)))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.3e-131], N[Not[LessEqual[z, 4.7e-150]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.30000000000000019e-131 or 4.6999999999999999e-150 < 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 86.4%

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

      1. neg-mul-1 86.4%

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

   7. Simplified 86.4%

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

   8. Taylor expanded in x around 0 86.4%

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

      1. cancel-sign-sub-inv 86.4%

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

      2. metadata-eval 86.4%

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

      3. *-lft-identity 86.4%

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

      4. +-commutative 86.4%

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

   10. Simplified 86.4%

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

   if -4.30000000000000019e-131 < z < 4.6999999999999999e-150

   1. Initial program 100.0%

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

      1. div-sub 90.3%

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

      2. sub-neg 90.3%

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

      3. distribute-frac-neg 90.3%

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

      4. +-commutative 90.3%

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

      5. associate-+r+ 90.3%

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

      6. distribute-frac-neg 90.3%

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

      7. sub-neg 90.3%

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

      8. associate--r- 90.3%

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

      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 inf 66.0%

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

      1. distribute-lft-out-- 66.0%

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

      2. *-rgt-identity 66.0%

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

      3. associate-*r/ 66.0%

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

      4. *-rgt-identity 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in z around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. distribute-frac-neg 66.0%

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

   10. Simplified 66.0%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-131} \lor \neg \left(z \leq 4.7 \cdot 10^{-150}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. div-sub 96.9%

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

   2. sub-neg 96.9%

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

   3. distribute-frac-neg 96.9%

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

   4. +-commutative 96.9%

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

   5. associate-+r+ 96.9%

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

   6. distribute-frac-neg 96.9%

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

   7. sub-neg 96.9%

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

   8. associate--r- 96.9%

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

   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 35.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024191 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))