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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 7

Speedup: 1.0×

• 20.4% 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: 56.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -6.1 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+74} \lor \neg \left(z \leq 1.9 \cdot 10^{+108}\right) \land z \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -6.1e+69)
     x
     (if (<= z -2.4e-77)
       (/ y z)
       (if (<= z -1.5e-182)
         t_0
         (if (<= z -3.3e-235)
           (/ y z)
           (if (<= z 2.1e-182)
             t_0
             (if (<= z 2.6e-161)
               (/ y z)
               (if (<= z 6e-39)
                 t_0
                 (if (or (<= z 4e+74)
                         (and (not (<= z 1.9e+108)) (<= z 3.8e+194)))
                   (/ y z)
                   x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -6.1e+69) {
		tmp = x;
	} else if (z <= -2.4e-77) {
		tmp = y / z;
	} else if (z <= -1.5e-182) {
		tmp = t_0;
	} else if (z <= -3.3e-235) {
		tmp = y / z;
	} else if (z <= 2.1e-182) {
		tmp = t_0;
	} else if (z <= 2.6e-161) {
		tmp = y / z;
	} else if (z <= 6e-39) {
		tmp = t_0;
	} else if ((z <= 4e+74) || (!(z <= 1.9e+108) && (z <= 3.8e+194))) {
		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 <= (-6.1d+69)) then
        tmp = x
    else if (z <= (-2.4d-77)) then
        tmp = y / z
    else if (z <= (-1.5d-182)) then
        tmp = t_0
    else if (z <= (-3.3d-235)) then
        tmp = y / z
    else if (z <= 2.1d-182) then
        tmp = t_0
    else if (z <= 2.6d-161) then
        tmp = y / z
    else if (z <= 6d-39) then
        tmp = t_0
    else if ((z <= 4d+74) .or. (.not. (z <= 1.9d+108)) .and. (z <= 3.8d+194)) 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 <= -6.1e+69) {
		tmp = x;
	} else if (z <= -2.4e-77) {
		tmp = y / z;
	} else if (z <= -1.5e-182) {
		tmp = t_0;
	} else if (z <= -3.3e-235) {
		tmp = y / z;
	} else if (z <= 2.1e-182) {
		tmp = t_0;
	} else if (z <= 2.6e-161) {
		tmp = y / z;
	} else if (z <= 6e-39) {
		tmp = t_0;
	} else if ((z <= 4e+74) || (!(z <= 1.9e+108) && (z <= 3.8e+194))) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -6.1e+69:
		tmp = x
	elif z <= -2.4e-77:
		tmp = y / z
	elif z <= -1.5e-182:
		tmp = t_0
	elif z <= -3.3e-235:
		tmp = y / z
	elif z <= 2.1e-182:
		tmp = t_0
	elif z <= 2.6e-161:
		tmp = y / z
	elif z <= 6e-39:
		tmp = t_0
	elif (z <= 4e+74) or (not (z <= 1.9e+108) and (z <= 3.8e+194)):
		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 <= -6.1e+69)
		tmp = x;
	elseif (z <= -2.4e-77)
		tmp = Float64(y / z);
	elseif (z <= -1.5e-182)
		tmp = t_0;
	elseif (z <= -3.3e-235)
		tmp = Float64(y / z);
	elseif (z <= 2.1e-182)
		tmp = t_0;
	elseif (z <= 2.6e-161)
		tmp = Float64(y / z);
	elseif (z <= 6e-39)
		tmp = t_0;
	elseif ((z <= 4e+74) || (!(z <= 1.9e+108) && (z <= 3.8e+194)))
		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 <= -6.1e+69)
		tmp = x;
	elseif (z <= -2.4e-77)
		tmp = y / z;
	elseif (z <= -1.5e-182)
		tmp = t_0;
	elseif (z <= -3.3e-235)
		tmp = y / z;
	elseif (z <= 2.1e-182)
		tmp = t_0;
	elseif (z <= 2.6e-161)
		tmp = y / z;
	elseif (z <= 6e-39)
		tmp = t_0;
	elseif ((z <= 4e+74) || (~((z <= 1.9e+108)) && (z <= 3.8e+194)))
		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, -6.1e+69], x, If[LessEqual[z, -2.4e-77], N[(y / z), $MachinePrecision], If[LessEqual[z, -1.5e-182], t$95$0, If[LessEqual[z, -3.3e-235], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.1e-182], t$95$0, If[LessEqual[z, 2.6e-161], N[(y / z), $MachinePrecision], If[LessEqual[z, 6e-39], t$95$0, If[Or[LessEqual[z, 4e+74], And[N[Not[LessEqual[z, 1.9e+108]], $MachinePrecision], LessEqual[z, 3.8e+194]]], N[(y / z), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.1000000000000001e69 or 3.99999999999999981e74 < z < 1.90000000000000004e108 or 3.7999999999999999e194 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 86.4%

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

   if -6.1000000000000001e69 < z < -2.3999999999999999e-77 or -1.5000000000000001e-182 < z < -3.30000000000000028e-235 or 2.1e-182 < z < 2.59999999999999995e-161 or 6.00000000000000055e-39 < z < 3.99999999999999981e74 or 1.90000000000000004e108 < z < 3.7999999999999999e194

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 67.4%

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

   if -2.3999999999999999e-77 < z < -1.5000000000000001e-182 or -3.30000000000000028e-235 < z < 2.1e-182 or 2.59999999999999995e-161 < z < 6.00000000000000055e-39

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 100.0%

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

   3. Taylor expanded in y around 0 67.1%

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

      1. mul-1-neg 67.1%

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

      2. distribute-neg-frac 67.1%

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

   5. Simplified 67.1%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.1 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-182}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-182}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+74} \lor \neg \left(z \leq 1.9 \cdot 10^{+108}\right) \land z \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 57.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{+74} \lor \neg \left(z \leq 2 \cdot 10^{+106}\right) \land z \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.8e+73)
   x
   (if (or (<= z 4.05e+74) (and (not (<= z 2e+106)) (<= z 3.8e+194)))
     (/ y z)
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.8e+73) {
		tmp = x;
	} else if ((z <= 4.05e+74) || (!(z <= 2e+106) && (z <= 3.8e+194))) {
		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 <= (-9.8d+73)) then
        tmp = x
    else if ((z <= 4.05d+74) .or. (.not. (z <= 2d+106)) .and. (z <= 3.8d+194)) 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 <= -9.8e+73) {
		tmp = x;
	} else if ((z <= 4.05e+74) || (!(z <= 2e+106) && (z <= 3.8e+194))) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.8e+73:
		tmp = x
	elif (z <= 4.05e+74) or (not (z <= 2e+106) and (z <= 3.8e+194)):
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.8e+73)
		tmp = x;
	elseif ((z <= 4.05e+74) || (!(z <= 2e+106) && (z <= 3.8e+194)))
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.8e+73)
		tmp = x;
	elseif ((z <= 4.05e+74) || (~((z <= 2e+106)) && (z <= 3.8e+194)))
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.8e+73], x, If[Or[LessEqual[z, 4.05e+74], And[N[Not[LessEqual[z, 2e+106]], $MachinePrecision], LessEqual[z, 3.8e+194]]], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -9.7999999999999998e73 or 4.0500000000000002e74 < z < 2.00000000000000018e106 or 3.7999999999999999e194 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 86.4%

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

   if -9.7999999999999998e73 < z < 4.0500000000000002e74 or 2.00000000000000018e106 < z < 3.7999999999999999e194

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 52.3%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+73}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.05 \cdot 10^{+74} \lor \neg \left(z \leq 2 \cdot 10^{+106}\right) \land z \leq 3.8 \cdot 10^{+194}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 72.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+128} \lor \neg \left(x \leq 4.2 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.3e+128) (not (<= x 4.2e+173))) (/ (- x) z) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.3e+128) || !(x <= 4.2e+173)) {
		tmp = -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 <= (-2.3d+128)) .or. (.not. (x <= 4.2d+173))) then
        tmp = -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 <= -2.3e+128) || !(x <= 4.2e+173)) {
		tmp = -x / z;
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.3e+128) or not (x <= 4.2e+173):
		tmp = -x / z
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.3e+128) || !(x <= 4.2e+173))
		tmp = Float64(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 <= -2.3e+128) || ~((x <= 4.2e+173)))
		tmp = -x / z;
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.3e+128], N[Not[LessEqual[x, 4.2e+173]], $MachinePrecision]], N[((-x) / z), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.29999999999999998e128 or 4.2e173 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 65.8%

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

   3. Taylor expanded in y around 0 66.0%

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

      1. mul-1-neg 66.0%

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

      2. distribute-neg-frac 66.0%

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

   5. Simplified 66.0%

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

   if -2.29999999999999998e128 < x < 4.2e173

   1. Initial program 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around inf 83.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+128} \lor \neg \left(x \leq 4.2 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 5: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+35} \lor \neg \left(x \leq 6.5 \cdot 10^{+47}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e+35) (not (<= x 6.5e+47))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+35) || !(x <= 6.5e+47)) {
		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 <= (-1.9d+35)) .or. (.not. (x <= 6.5d+47))) 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 <= -1.9e+35) || !(x <= 6.5e+47)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e+35) or not (x <= 6.5e+47):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e+35) || !(x <= 6.5e+47))
		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 <= -1.9e+35) || ~((x <= 6.5e+47)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e+35], N[Not[LessEqual[x, 6.5e+47]], $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 < -1.9e35 or 6.49999999999999988e47 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 90.7%

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

      1. sub-neg 90.7%

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

      2. distribute-rgt-in 90.7%

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

      3. *-lft-identity 90.7%

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

      4. distribute-lft-neg-in 90.7%

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

      5. associate-*l/ 90.8%

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

      6. *-lft-identity 90.8%

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

      7. mul-1-neg 90.8%

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

      8. mul-1-neg 90.8%

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

      9. sub-neg 90.8%

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

   4. Simplified 90.8%

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

   if -1.9e35 < x < 6.49999999999999988e47

   1. Initial program 100.0%

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

      1. clear-num 99.7%

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

      2. inv-pow 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around inf 87.5%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+35} \lor \neg \left(x \leq 6.5 \cdot 10^{+47}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -13.2 \lor \neg \left(z \leq 9.8 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -13.2) (not (<= z 9.8e-6))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -13.2) || !(z <= 9.8e-6)) {
		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 <= (-13.2d0)) .or. (.not. (z <= 9.8d-6))) 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 <= -13.2) || !(z <= 9.8e-6)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -13.2) or not (z <= 9.8e-6):
		tmp = x + (y / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -13.2) || !(z <= 9.8e-6))
		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 <= -13.2) || ~((z <= 9.8e-6)))
		tmp = x + (y / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -13.2], N[Not[LessEqual[z, 9.8e-6]], $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 < -13.199999999999999 or 9.79999999999999934e-6 < z

   1. Initial program 100.0%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 98.2%

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

   if -13.199999999999999 < z < 9.79999999999999934e-6

   1. Initial program 100.0%

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

   2. 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 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -13.2 \lor \neg \left(z \leq 9.8 \cdot 10^{-6}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 7: 36.4% 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 2023301 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))