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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 7

Speedup: 1.0×

• 20.8% 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: 61.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -330000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-123}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-289}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-253}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-177}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.00215:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -330000.0)
     x
     (if (<= z -2.3e-55)
       (/ y z)
       (if (<= z -7.5e-123)
         t_0
         (if (<= z -1.1e-195)
           (/ y z)
           (if (<= z 1.25e-289)
             t_0
             (if (<= z 1.9e-253)
               (/ y z)
               (if (<= z 1.15e-177)
                 t_0
                 (if (<= z 4.4e-85)
                   (/ y z)
                   (if (<= z 0.00215)
                     t_0
                     (if (<= z 2.4e+25) (/ y z) x))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -330000.0) {
		tmp = x;
	} else if (z <= -2.3e-55) {
		tmp = y / z;
	} else if (z <= -7.5e-123) {
		tmp = t_0;
	} else if (z <= -1.1e-195) {
		tmp = y / z;
	} else if (z <= 1.25e-289) {
		tmp = t_0;
	} else if (z <= 1.9e-253) {
		tmp = y / z;
	} else if (z <= 1.15e-177) {
		tmp = t_0;
	} else if (z <= 4.4e-85) {
		tmp = y / z;
	} else if (z <= 0.00215) {
		tmp = t_0;
	} else if (z <= 2.4e+25) {
		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 <= (-330000.0d0)) then
        tmp = x
    else if (z <= (-2.3d-55)) then
        tmp = y / z
    else if (z <= (-7.5d-123)) then
        tmp = t_0
    else if (z <= (-1.1d-195)) then
        tmp = y / z
    else if (z <= 1.25d-289) then
        tmp = t_0
    else if (z <= 1.9d-253) then
        tmp = y / z
    else if (z <= 1.15d-177) then
        tmp = t_0
    else if (z <= 4.4d-85) then
        tmp = y / z
    else if (z <= 0.00215d0) then
        tmp = t_0
    else if (z <= 2.4d+25) 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 <= -330000.0) {
		tmp = x;
	} else if (z <= -2.3e-55) {
		tmp = y / z;
	} else if (z <= -7.5e-123) {
		tmp = t_0;
	} else if (z <= -1.1e-195) {
		tmp = y / z;
	} else if (z <= 1.25e-289) {
		tmp = t_0;
	} else if (z <= 1.9e-253) {
		tmp = y / z;
	} else if (z <= 1.15e-177) {
		tmp = t_0;
	} else if (z <= 4.4e-85) {
		tmp = y / z;
	} else if (z <= 0.00215) {
		tmp = t_0;
	} else if (z <= 2.4e+25) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -330000.0:
		tmp = x
	elif z <= -2.3e-55:
		tmp = y / z
	elif z <= -7.5e-123:
		tmp = t_0
	elif z <= -1.1e-195:
		tmp = y / z
	elif z <= 1.25e-289:
		tmp = t_0
	elif z <= 1.9e-253:
		tmp = y / z
	elif z <= 1.15e-177:
		tmp = t_0
	elif z <= 4.4e-85:
		tmp = y / z
	elif z <= 0.00215:
		tmp = t_0
	elif z <= 2.4e+25:
		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 <= -330000.0)
		tmp = x;
	elseif (z <= -2.3e-55)
		tmp = Float64(y / z);
	elseif (z <= -7.5e-123)
		tmp = t_0;
	elseif (z <= -1.1e-195)
		tmp = Float64(y / z);
	elseif (z <= 1.25e-289)
		tmp = t_0;
	elseif (z <= 1.9e-253)
		tmp = Float64(y / z);
	elseif (z <= 1.15e-177)
		tmp = t_0;
	elseif (z <= 4.4e-85)
		tmp = Float64(y / z);
	elseif (z <= 0.00215)
		tmp = t_0;
	elseif (z <= 2.4e+25)
		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 <= -330000.0)
		tmp = x;
	elseif (z <= -2.3e-55)
		tmp = y / z;
	elseif (z <= -7.5e-123)
		tmp = t_0;
	elseif (z <= -1.1e-195)
		tmp = y / z;
	elseif (z <= 1.25e-289)
		tmp = t_0;
	elseif (z <= 1.9e-253)
		tmp = y / z;
	elseif (z <= 1.15e-177)
		tmp = t_0;
	elseif (z <= 4.4e-85)
		tmp = y / z;
	elseif (z <= 0.00215)
		tmp = t_0;
	elseif (z <= 2.4e+25)
		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, -330000.0], x, If[LessEqual[z, -2.3e-55], N[(y / z), $MachinePrecision], If[LessEqual[z, -7.5e-123], t$95$0, If[LessEqual[z, -1.1e-195], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.25e-289], t$95$0, If[LessEqual[z, 1.9e-253], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.15e-177], t$95$0, If[LessEqual[z, 4.4e-85], N[(y / z), $MachinePrecision], If[LessEqual[z, 0.00215], t$95$0, If[LessEqual[z, 2.4e+25], N[(y / z), $MachinePrecision], x]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3e5 or 2.39999999999999996e25 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 72.9%

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

   if -3.3e5 < z < -2.30000000000000011e-55 or -7.50000000000000011e-123 < z < -1.10000000000000003e-195 or 1.25000000000000007e-289 < z < 1.90000000000000006e-253 or 1.15000000000000011e-177 < z < 4.4e-85 or 0.00215 < z < 2.39999999999999996e25

   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/ 99.7%

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

      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 78.8%

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

   if -2.30000000000000011e-55 < z < -7.50000000000000011e-123 or -1.10000000000000003e-195 < z < 1.25000000000000007e-289 or 1.90000000000000006e-253 < z < 1.15000000000000011e-177 or 4.4e-85 < z < 0.00215

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.6%

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

   3. Taylor expanded in z around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. distribute-frac-neg 76.4%

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

   5. Simplified 76.4%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -330000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-195}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-289}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-253}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-177}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.00215:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-92} \lor \neg \left(y \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.7e-92) (not (<= y 2.3e-65))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.7e-92) || !(y <= 2.3e-65)) {
		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 <= (-3.7d-92)) .or. (.not. (y <= 2.3d-65))) 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 <= -3.7e-92) || !(y <= 2.3e-65)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.7e-92) or not (y <= 2.3e-65):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.7e-92) || !(y <= 2.3e-65))
		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 <= -3.7e-92) || ~((y <= 2.3e-65)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.7e-92], N[Not[LessEqual[y, 2.3e-65]], $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 < -3.69999999999999977e-92 or 2.3e-65 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.3%

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

   if -3.69999999999999977e-92 < y < 2.3e-65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-92} \lor \neg \left(y \leq 2.3 \cdot 10^{-65}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -110000 \lor \neg \left(z \leq 0.00215\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -110000.0) (not (<= z 0.00215))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -110000.0) || !(z <= 0.00215)) {
		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 <= (-110000.0d0)) .or. (.not. (z <= 0.00215d0))) 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 <= -110000.0) || !(z <= 0.00215)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -110000.0) or not (z <= 0.00215):
		tmp = x + (y / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -110000.0) || !(z <= 0.00215))
		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 <= -110000.0) || ~((z <= 0.00215)))
		tmp = x + (y / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -110000.0], N[Not[LessEqual[z, 0.00215]], $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 < -1.1e5 or 0.00215 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.2%

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

   if -1.1e5 < z < 0.00215

   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/ 99.8%

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

      4. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in z around 0 99.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -110000 \lor \neg \left(z \leq 0.00215\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 5: 61.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -220000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -220000.0) x (if (<= z 2.4e+25) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -220000.0) {
		tmp = x;
	} else if (z <= 2.4e+25) {
		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 <= (-220000.0d0)) then
        tmp = x
    else if (z <= 2.4d+25) 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 <= -220000.0) {
		tmp = x;
	} else if (z <= 2.4e+25) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -220000.0:
		tmp = x
	elif z <= 2.4e+25:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -220000.0)
		tmp = x;
	elseif (z <= 2.4e+25)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -220000.0)
		tmp = x;
	elseif (z <= 2.4e+25)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -220000.0], x, If[LessEqual[z, 2.4e+25], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e5 or 2.39999999999999996e25 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 72.9%

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

   if -2.2e5 < z < 2.39999999999999996e25

   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/ 99.7%

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

      4. fma-def 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 52.6%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -220000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{+184}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x 1.4e+184) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 1.4e+184) {
		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 (x <= 1.4d+184) 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 (x <= 1.4e+184) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 1.4e+184:
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 1.4e+184)
		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 (x <= 1.4e+184)
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 1.4e+184], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.39999999999999995e184

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.6%

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

   if 1.39999999999999995e184 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 100.0%

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

   3. Taylor expanded in z around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. distribute-frac-neg 66.9%

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

   5. Simplified 66.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.4 \cdot 10^{+184}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 7: 36.0% 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 37.1%

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

3. Final simplification 37.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))