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

Percentage Accurate: 100.0% → 100.0%

Time: 7.4s

Alternatives: 7

Speedup: 1.0×

• 20.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]

2. Final simplification 100.0%

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

Alternative 2: 60.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-70}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e+133)
   x
   (if (<= z -6.5e+88)
     (/ y z)
     (if (<= z -3.6e+54)
       x
       (if (<= z -1.32e-55)
         (/ y z)
         (if (<= z 2.1e-70) (/ (- x) z) (if (<= z 3.5e+21) (/ y z) x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+133) {
		tmp = x;
	} else if (z <= -6.5e+88) {
		tmp = y / z;
	} else if (z <= -3.6e+54) {
		tmp = x;
	} else if (z <= -1.32e-55) {
		tmp = y / z;
	} else if (z <= 2.1e-70) {
		tmp = -x / z;
	} else if (z <= 3.5e+21) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.1d+133)) then
        tmp = x
    else if (z <= (-6.5d+88)) then
        tmp = y / z
    else if (z <= (-3.6d+54)) then
        tmp = x
    else if (z <= (-1.32d-55)) then
        tmp = y / z
    else if (z <= 2.1d-70) then
        tmp = -x / z
    else if (z <= 3.5d+21) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+133) {
		tmp = x;
	} else if (z <= -6.5e+88) {
		tmp = y / z;
	} else if (z <= -3.6e+54) {
		tmp = x;
	} else if (z <= -1.32e-55) {
		tmp = y / z;
	} else if (z <= 2.1e-70) {
		tmp = -x / z;
	} else if (z <= 3.5e+21) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e+133:
		tmp = x
	elif z <= -6.5e+88:
		tmp = y / z
	elif z <= -3.6e+54:
		tmp = x
	elif z <= -1.32e-55:
		tmp = y / z
	elif z <= 2.1e-70:
		tmp = -x / z
	elif z <= 3.5e+21:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e+133)
		tmp = x;
	elseif (z <= -6.5e+88)
		tmp = Float64(y / z);
	elseif (z <= -3.6e+54)
		tmp = x;
	elseif (z <= -1.32e-55)
		tmp = Float64(y / z);
	elseif (z <= 2.1e-70)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 3.5e+21)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e+133)
		tmp = x;
	elseif (z <= -6.5e+88)
		tmp = y / z;
	elseif (z <= -3.6e+54)
		tmp = x;
	elseif (z <= -1.32e-55)
		tmp = y / z;
	elseif (z <= 2.1e-70)
		tmp = -x / z;
	elseif (z <= 3.5e+21)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e+133], x, If[LessEqual[z, -6.5e+88], N[(y / z), $MachinePrecision], If[LessEqual[z, -3.6e+54], x, If[LessEqual[z, -1.32e-55], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.1e-70], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 3.5e+21], N[(y / z), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.10000000000000004e133 or -6.5000000000000002e88 < z < -3.6000000000000001e54 or 3.5e21 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around inf 74.3%

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

   if -4.10000000000000004e133 < z < -6.5000000000000002e88 or -3.6000000000000001e54 < z < -1.31999999999999993e-55 or 2.1000000000000001e-70 < z < 3.5e21

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. div-sub 100.0%

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

      3. associate-+l- 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around inf 67.0%

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

   if -1.31999999999999993e-55 < z < 2.1000000000000001e-70

   1. Initial program 99.9%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around inf 65.3%

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

   3. Taylor expanded in z around 0 65.5%

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

      1. neg-mul-1 65.5%

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

      2. distribute-neg-frac 65.5%

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

   5. Simplified 65.5%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-70}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 60.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e+133)
   x
   (if (<= z -7e+88)
     (/ y z)
     (if (<= z -3.7e+53) x (if (<= z 1.15e+21) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+133) {
		tmp = x;
	} else if (z <= -7e+88) {
		tmp = y / z;
	} else if (z <= -3.7e+53) {
		tmp = x;
	} else if (z <= 1.15e+21) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.1d+133)) then
        tmp = x
    else if (z <= (-7d+88)) then
        tmp = y / z
    else if (z <= (-3.7d+53)) then
        tmp = x
    else if (z <= 1.15d+21) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+133) {
		tmp = x;
	} else if (z <= -7e+88) {
		tmp = y / z;
	} else if (z <= -3.7e+53) {
		tmp = x;
	} else if (z <= 1.15e+21) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e+133:
		tmp = x
	elif z <= -7e+88:
		tmp = y / z
	elif z <= -3.7e+53:
		tmp = x
	elif z <= 1.15e+21:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e+133)
		tmp = x;
	elseif (z <= -7e+88)
		tmp = Float64(y / z);
	elseif (z <= -3.7e+53)
		tmp = x;
	elseif (z <= 1.15e+21)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e+133)
		tmp = x;
	elseif (z <= -7e+88)
		tmp = y / z;
	elseif (z <= -3.7e+53)
		tmp = x;
	elseif (z <= 1.15e+21)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e+133], x, If[LessEqual[z, -7e+88], N[(y / z), $MachinePrecision], If[LessEqual[z, -3.7e+53], x, If[LessEqual[z, 1.15e+21], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000004e133 or -6.9999999999999995e88 < z < -3.7e53 or 1.15e21 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in z around inf 74.3%

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

   if -4.10000000000000004e133 < z < -6.9999999999999995e88 or -3.7e53 < z < 1.15e21

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. div-sub 98.0%

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

      3. associate-+l- 98.0%

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

   3. Applied egg-rr 98.0%

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

   4. Taylor expanded in y around inf 50.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+133}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+88}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+21}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-50} \lor \neg \left(z \leq 8.8 \cdot 10^{-71}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.5e-50) (not (<= z 8.8e-71))) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.5e-50) || !(z <= 8.8e-71)) {
		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 <= (-1.5d-50)) .or. (.not. (z <= 8.8d-71))) 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 <= -1.5e-50) || !(z <= 8.8e-71)) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.5e-50) or not (z <= 8.8e-71):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.5e-50) || !(z <= 8.8e-71))
		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 <= -1.5e-50) || ~((z <= 8.8e-71)))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.5e-50], N[Not[LessEqual[z, 8.8e-71]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999995e-50 or 8.7999999999999999e-71 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in y around inf 91.3%

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

   if -1.49999999999999995e-50 < z < 8.7999999999999999e-71

   1. Initial program 99.9%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in x around inf 65.3%

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

   3. Taylor expanded in z around 0 65.5%

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

      1. neg-mul-1 65.5%

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

      2. distribute-neg-frac 65.5%

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

   5. Simplified 65.5%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-50} \lor \neg \left(z \leq 8.8 \cdot 10^{-71}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 5: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-113} \lor \neg \left(y \leq 2.4 \cdot 10^{-108}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.8e-113) (not (<= y 2.4e-108))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.8e-113) || !(y <= 2.4e-108)) {
		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 <= (-7.8d-113)) .or. (.not. (y <= 2.4d-108))) 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 <= -7.8e-113) || !(y <= 2.4e-108)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.8e-113) or not (y <= 2.4e-108):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.8e-113) || !(y <= 2.4e-108))
		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 <= -7.8e-113) || ~((y <= 2.4e-108)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.8e-113], N[Not[LessEqual[y, 2.4e-108]], $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 < -7.7999999999999997e-113 or 2.40000000000000017e-108 < y

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in y around inf 83.4%

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

   if -7.7999999999999997e-113 < y < 2.40000000000000017e-108

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in y around 0 94.6%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-113} \lor \neg \left(y \leq 2.4 \cdot 10^{-108}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 6: 98.9% accurate, 0.8× 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. Taylor expanded in y around inf 98.9%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. div-sub 97.7%

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

      3. associate-+l- 97.7%

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

   3. Applied egg-rr 97.7%

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

   4. Taylor expanded in z around 0 97.4%

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

4. Final simplification 98.2%

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

Alternative 7: 37.4% 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. Taylor expanded in z around inf 34.0%

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

3. Final simplification 34.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))