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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

Alternatives: 6

Speedup: 1.0×

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: 60.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-96}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-188}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-286}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-136}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -2.9e+14)
     x
     (if (<= z -5.7e-96)
       (/ y z)
       (if (<= z -2.8e-188)
         t_0
         (if (<= z -1.45e-286)
           (/ y z)
           (if (<= z 4.9e-225)
             t_0
             (if (<= z 7.8e-143)
               (/ y z)
               (if (<= z 1.25e-136) t_0 (if (<= z 7.6e+116) (/ y z) x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -2.9e+14) {
		tmp = x;
	} else if (z <= -5.7e-96) {
		tmp = y / z;
	} else if (z <= -2.8e-188) {
		tmp = t_0;
	} else if (z <= -1.45e-286) {
		tmp = y / z;
	} else if (z <= 4.9e-225) {
		tmp = t_0;
	} else if (z <= 7.8e-143) {
		tmp = y / z;
	} else if (z <= 1.25e-136) {
		tmp = t_0;
	} else if (z <= 7.6e+116) {
		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 <= (-2.9d+14)) then
        tmp = x
    else if (z <= (-5.7d-96)) then
        tmp = y / z
    else if (z <= (-2.8d-188)) then
        tmp = t_0
    else if (z <= (-1.45d-286)) then
        tmp = y / z
    else if (z <= 4.9d-225) then
        tmp = t_0
    else if (z <= 7.8d-143) then
        tmp = y / z
    else if (z <= 1.25d-136) then
        tmp = t_0
    else if (z <= 7.6d+116) 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 <= -2.9e+14) {
		tmp = x;
	} else if (z <= -5.7e-96) {
		tmp = y / z;
	} else if (z <= -2.8e-188) {
		tmp = t_0;
	} else if (z <= -1.45e-286) {
		tmp = y / z;
	} else if (z <= 4.9e-225) {
		tmp = t_0;
	} else if (z <= 7.8e-143) {
		tmp = y / z;
	} else if (z <= 1.25e-136) {
		tmp = t_0;
	} else if (z <= 7.6e+116) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -2.9e+14:
		tmp = x
	elif z <= -5.7e-96:
		tmp = y / z
	elif z <= -2.8e-188:
		tmp = t_0
	elif z <= -1.45e-286:
		tmp = y / z
	elif z <= 4.9e-225:
		tmp = t_0
	elif z <= 7.8e-143:
		tmp = y / z
	elif z <= 1.25e-136:
		tmp = t_0
	elif z <= 7.6e+116:
		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 <= -2.9e+14)
		tmp = x;
	elseif (z <= -5.7e-96)
		tmp = Float64(y / z);
	elseif (z <= -2.8e-188)
		tmp = t_0;
	elseif (z <= -1.45e-286)
		tmp = Float64(y / z);
	elseif (z <= 4.9e-225)
		tmp = t_0;
	elseif (z <= 7.8e-143)
		tmp = Float64(y / z);
	elseif (z <= 1.25e-136)
		tmp = t_0;
	elseif (z <= 7.6e+116)
		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 <= -2.9e+14)
		tmp = x;
	elseif (z <= -5.7e-96)
		tmp = y / z;
	elseif (z <= -2.8e-188)
		tmp = t_0;
	elseif (z <= -1.45e-286)
		tmp = y / z;
	elseif (z <= 4.9e-225)
		tmp = t_0;
	elseif (z <= 7.8e-143)
		tmp = y / z;
	elseif (z <= 1.25e-136)
		tmp = t_0;
	elseif (z <= 7.6e+116)
		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, -2.9e+14], x, If[LessEqual[z, -5.7e-96], N[(y / z), $MachinePrecision], If[LessEqual[z, -2.8e-188], t$95$0, If[LessEqual[z, -1.45e-286], N[(y / z), $MachinePrecision], If[LessEqual[z, 4.9e-225], t$95$0, If[LessEqual[z, 7.8e-143], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.25e-136], t$95$0, If[LessEqual[z, 7.6e+116], N[(y / z), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e14 or 7.5999999999999998e116 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 76.9%

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

   if -2.9e14 < z < -5.70000000000000009e-96 or -2.8000000000000001e-188 < z < -1.4499999999999999e-286 or 4.89999999999999971e-225 < z < 7.80000000000000007e-143 or 1.25e-136 < z < 7.5999999999999998e116

   1. Initial program 100.0%

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

      1. flip-+ 31.5%

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

      2. div-inv 31.4%

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

      3. pow2 31.4%

         \[\leadsto \left(x \cdot x - \color{blue}{{\left(\frac{y - x}{z}\right)}^{2}}\right) \cdot \frac{1}{x - \frac{y - x}{z}} \]

   3. Applied egg-rr 31.4%

      \[\leadsto \color{blue}{\left(x \cdot x - {\left(\frac{y - x}{z}\right)}^{2}\right) \cdot \frac{1}{x - \frac{y - x}{z}}} \]

   4. Taylor expanded in x around 0 60.7%

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

   if -5.70000000000000009e-96 < z < -2.8000000000000001e-188 or -1.4499999999999999e-286 < z < 4.89999999999999971e-225 or 7.80000000000000007e-143 < z < 1.25e-136

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.4%

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

   3. Taylor expanded in z around 0 76.7%

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

      1. mul-1-neg 76.7%

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

      2. distribute-frac-neg 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-96}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-188}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-286}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-225}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-136}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-234} \lor \neg \left(y \leq 3.9 \cdot 10^{-158}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.3e-234) (not (<= y 3.9e-158))) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.3e-234) || !(y <= 3.9e-158)) {
		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 ((y <= (-3.3d-234)) .or. (.not. (y <= 3.9d-158))) 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 ((y <= -3.3e-234) || !(y <= 3.9e-158)) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.3e-234) or not (y <= 3.9e-158):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.3e-234) || !(y <= 3.9e-158))
		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 ((y <= -3.3e-234) || ~((y <= 3.9e-158)))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.3e-234], N[Not[LessEqual[y, 3.9e-158]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.30000000000000014e-234 or 3.8999999999999997e-158 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.1%

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

   if -3.30000000000000014e-234 < y < 3.8999999999999997e-158

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 92.9%

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

   3. Taylor expanded in z around 0 61.8%

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

      1. mul-1-neg 61.8%

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

      2. distribute-frac-neg 61.8%

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

   5. Simplified 61.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-234} \lor \neg \left(y \leq 3.9 \cdot 10^{-158}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 4: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+56} \lor \neg \left(x \leq 2.4 \cdot 10^{-48}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.3e+56) (not (<= x 2.4e-48))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.3e+56) || !(x <= 2.4e-48)) {
		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 <= (-1.3d+56)) .or. (.not. (x <= 2.4d-48))) 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 <= -1.3e+56) || !(x <= 2.4e-48)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.3e+56) or not (x <= 2.4e-48):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.3e+56) || !(x <= 2.4e-48))
		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 <= -1.3e+56) || ~((x <= 2.4e-48)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.3e+56], N[Not[LessEqual[x, 2.4e-48]], $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 < -1.30000000000000005e56 or 2.4e-48 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.3%

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

   if -1.30000000000000005e56 < x < 2.4e-48

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 86.7%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+56} \lor \neg \left(x \leq 2.4 \cdot 10^{-48}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 5: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.6e+16) x (if (<= z 8e+116) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.6e+16) {
		tmp = x;
	} else if (z <= 8e+116) {
		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 <= (-9.6d+16)) then
        tmp = x
    else if (z <= 8d+116) 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 <= -9.6e+16) {
		tmp = x;
	} else if (z <= 8e+116) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.6e+16:
		tmp = x
	elif z <= 8e+116:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.6e+16)
		tmp = x;
	elseif (z <= 8e+116)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.6e+16)
		tmp = x;
	elseif (z <= 8e+116)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.6e+16], x, If[LessEqual[z, 8e+116], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.6e16 or 8.00000000000000012e116 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 76.9%

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

   if -9.6e16 < z < 8.00000000000000012e116

   1. Initial program 100.0%

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

      1. flip-+ 27.8%

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

      2. div-inv 27.7%

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

      3. pow2 27.7%

         \[\leadsto \left(x \cdot x - \color{blue}{{\left(\frac{y - x}{z}\right)}^{2}}\right) \cdot \frac{1}{x - \frac{y - x}{z}} \]

   3. Applied egg-rr 27.7%

      \[\leadsto \color{blue}{\left(x \cdot x - {\left(\frac{y - x}{z}\right)}^{2}\right) \cdot \frac{1}{x - \frac{y - x}{z}}} \]

   4. Taylor expanded in x around 0 51.3%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 37.0% 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 33.3%

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

3. Final simplification 33.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))