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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

Alternatives: 7

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 61.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.12e-9)
     x
     (if (<= z -1.4e-127)
       t_0
       (if (<= z -6.8e-165)
         (/ y z)
         (if (<= z -5.6e-253) t_0 (if (<= z 2.55e+36) (/ y z) x)))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.12e-9) {
		tmp = x;
	} else if (z <= -1.4e-127) {
		tmp = t_0;
	} else if (z <= -6.8e-165) {
		tmp = y / z;
	} else if (z <= -5.6e-253) {
		tmp = t_0;
	} else if (z <= 2.55e+36) {
		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) :: t_0
    real(8) :: tmp
    t_0 = -x / z
    if (z <= (-1.12d-9)) then
        tmp = x
    else if (z <= (-1.4d-127)) then
        tmp = t_0
    else if (z <= (-6.8d-165)) then
        tmp = y / z
    else if (z <= (-5.6d-253)) then
        tmp = t_0
    else if (z <= 2.55d+36) 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 t_0 = -x / z;
	double tmp;
	if (z <= -1.12e-9) {
		tmp = x;
	} else if (z <= -1.4e-127) {
		tmp = t_0;
	} else if (z <= -6.8e-165) {
		tmp = y / z;
	} else if (z <= -5.6e-253) {
		tmp = t_0;
	} else if (z <= 2.55e+36) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.12e-9:
		tmp = x
	elif z <= -1.4e-127:
		tmp = t_0
	elif z <= -6.8e-165:
		tmp = y / z
	elif z <= -5.6e-253:
		tmp = t_0
	elif z <= 2.55e+36:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -1.12e-9)
		tmp = x;
	elseif (z <= -1.4e-127)
		tmp = t_0;
	elseif (z <= -6.8e-165)
		tmp = Float64(y / z);
	elseif (z <= -5.6e-253)
		tmp = t_0;
	elseif (z <= 2.55e+36)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -1.12e-9)
		tmp = x;
	elseif (z <= -1.4e-127)
		tmp = t_0;
	elseif (z <= -6.8e-165)
		tmp = y / z;
	elseif (z <= -5.6e-253)
		tmp = t_0;
	elseif (z <= 2.55e+36)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -1.12e-9], x, If[LessEqual[z, -1.4e-127], t$95$0, If[LessEqual[z, -6.8e-165], N[(y / z), $MachinePrecision], If[LessEqual[z, -5.6e-253], t$95$0, If[LessEqual[z, 2.55e+36], N[(y / z), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.12000000000000006e-9 or 2.54999999999999986e36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.0%

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

   if -1.12000000000000006e-9 < z < -1.4e-127 or -6.8e-165 < z < -5.60000000000000011e-253

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 66.4%

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

   3. Taylor expanded in z around 0 66.4%

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

      1. neg-mul-1 66.4%

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

      2. distribute-frac-neg 66.4%

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

   5. Simplified 66.4%

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

   if -1.4e-127 < z < -6.8e-165 or -5.60000000000000011e-253 < z < 2.54999999999999986e36

   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. clear-num 99.7%

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

      3. associate-/r/ 99.6%

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

      4. fma-def 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   3. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 64.7%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-127}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-165}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-253}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-97} \lor \neg \left(z \leq -7.6 \cdot 10^{-128} \lor \neg \left(z \leq -4.7 \cdot 10^{-177}\right) \land z \leq -3.2 \cdot 10^{-215}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e-97)
         (not
          (or (<= z -7.6e-128) (and (not (<= z -4.7e-177)) (<= z -3.2e-215)))))
   (+ x (/ y z))
   (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-97) || !((z <= -7.6e-128) || (!(z <= -4.7e-177) && (z <= -3.2e-215)))) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.4d-97)) .or. (.not. (z <= (-7.6d-128)) .or. (.not. (z <= (-4.7d-177))) .and. (z <= (-3.2d-215)))) then
        tmp = x + (y / z)
    else
        tmp = -x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-97) || !((z <= -7.6e-128) || (!(z <= -4.7e-177) && (z <= -3.2e-215)))) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.4e-97) or not ((z <= -7.6e-128) or (not (z <= -4.7e-177) and (z <= -3.2e-215))):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.4e-97) || !((z <= -7.6e-128) || (!(z <= -4.7e-177) && (z <= -3.2e-215))))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.4e-97) || ~(((z <= -7.6e-128) || (~((z <= -4.7e-177)) && (z <= -3.2e-215)))))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e-97], N[Not[Or[LessEqual[z, -7.6e-128], And[N[Not[LessEqual[z, -4.7e-177]], $MachinePrecision], LessEqual[z, -3.2e-215]]]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999998e-97 or -7.6000000000000005e-128 < z < -4.69999999999999967e-177 or -3.2000000000000001e-215 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.0%

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

   if -4.3999999999999998e-97 < z < -7.6000000000000005e-128 or -4.69999999999999967e-177 < z < -3.2000000000000001e-215

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.5%

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

   3. Taylor expanded in z around 0 87.5%

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

      1. neg-mul-1 87.5%

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

      2. distribute-frac-neg 87.5%

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

   5. Simplified 87.5%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-97} \lor \neg \left(z \leq -7.6 \cdot 10^{-128} \lor \neg \left(z \leq -4.7 \cdot 10^{-177}\right) \land z \leq -3.2 \cdot 10^{-215}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1020000000 \lor \neg \left(x \leq 8 \cdot 10^{+159}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1020000000.0) (not (<= x 8e+159)))
   (- x (/ x z))
   (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1020000000.0) || !(x <= 8e+159)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1020000000.0d0)) .or. (.not. (x <= 8d+159))) then
        tmp = x - (x / z)
    else
        tmp = x + (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1020000000.0) || !(x <= 8e+159)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1020000000.0) or not (x <= 8e+159):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1020000000.0) || !(x <= 8e+159))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(x + Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1020000000.0) || ~((x <= 8e+159)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1020000000.0], N[Not[LessEqual[x, 8e+159]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e9 or 7.9999999999999994e159 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 92.2%

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

   if -1.02e9 < x < 7.9999999999999994e159

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1020000000 \lor \neg \left(x \leq 8 \cdot 10^{+159}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 5: 99.0% 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 98.4%

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

   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. clear-num 99.8%

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

      3. associate-/r/ 99.7%

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

      4. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

4. Final simplification 99.2%

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

Alternative 6: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -11:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -11.0) x (if (<= z 7.2e+36) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -11.0) {
		tmp = x;
	} else if (z <= 7.2e+36) {
		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 <= (-11.0d0)) then
        tmp = x
    else if (z <= 7.2d+36) 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 <= -11.0) {
		tmp = x;
	} else if (z <= 7.2e+36) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -11.0:
		tmp = x
	elif z <= 7.2e+36:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -11.0)
		tmp = x;
	elseif (z <= 7.2e+36)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -11.0)
		tmp = x;
	elseif (z <= 7.2e+36)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -11.0], x, If[LessEqual[z, 7.2e+36], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -11 or 7.1999999999999995e36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 74.2%

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

   if -11 < z < 7.1999999999999995e36

   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. clear-num 99.7%

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

      3. associate-/r/ 99.7%

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

      4. fma-def 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   3. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 55.1%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -11:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 36.1% 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. Taylor expanded in z around inf 35.7%

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

3. Final simplification 35.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))