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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 7

Speedup: 1.0×

• 20.9% 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: 62.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-208}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-44}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e+21)
   x
   (if (<= z 6.4e-208)
     (/ y z)
     (if (<= z 4.4e-44) (/ (- x) z) (if (<= z 9.2e+46) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e+21) {
		tmp = x;
	} else if (z <= 6.4e-208) {
		tmp = y / z;
	} else if (z <= 4.4e-44) {
		tmp = -x / z;
	} else if (z <= 9.2e+46) {
		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 <= (-2.5d+21)) then
        tmp = x
    else if (z <= 6.4d-208) then
        tmp = y / z
    else if (z <= 4.4d-44) then
        tmp = -x / z
    else if (z <= 9.2d+46) 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 <= -2.5e+21) {
		tmp = x;
	} else if (z <= 6.4e-208) {
		tmp = y / z;
	} else if (z <= 4.4e-44) {
		tmp = -x / z;
	} else if (z <= 9.2e+46) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e+21:
		tmp = x
	elif z <= 6.4e-208:
		tmp = y / z
	elif z <= 4.4e-44:
		tmp = -x / z
	elif z <= 9.2e+46:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e+21)
		tmp = x;
	elseif (z <= 6.4e-208)
		tmp = Float64(y / z);
	elseif (z <= 4.4e-44)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 9.2e+46)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e+21)
		tmp = x;
	elseif (z <= 6.4e-208)
		tmp = y / z;
	elseif (z <= 4.4e-44)
		tmp = -x / z;
	elseif (z <= 9.2e+46)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e+21], x, If[LessEqual[z, 6.4e-208], N[(y / z), $MachinePrecision], If[LessEqual[z, 4.4e-44], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 9.2e+46], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.5e21 or 9.2000000000000002e46 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.1%

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

   if -2.5e21 < z < 6.4000000000000003e-208 or 4.40000000000000024e-44 < z < 9.2000000000000002e46

   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 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 z around 0 90.3%

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

   5. Taylor expanded in y around inf 61.7%

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

   if 6.4000000000000003e-208 < z < 4.40000000000000024e-44

   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 z around 0 100.0%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-frac-neg 70.6%

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

   7. Simplified 70.6%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+21}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-208}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-44}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-207} \lor \neg \left(z \leq 2.05 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 5e-207) (not (<= z 2.05e-42))) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 5e-207) || !(z <= 2.05e-42)) {
		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 <= 5d-207) .or. (.not. (z <= 2.05d-42))) 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 <= 5e-207) || !(z <= 2.05e-42)) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 5e-207) or not (z <= 2.05e-42):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 5e-207) || !(z <= 2.05e-42))
		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 <= 5e-207) || ~((z <= 2.05e-42)))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 5e-207], N[Not[LessEqual[z, 2.05e-42]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.00000000000000014e-207 or 2.0500000000000001e-42 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 85.0%

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

   if 5.00000000000000014e-207 < z < 2.0500000000000001e-42

   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 z around 0 100.0%

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

   5. Taylor expanded in y around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. distribute-frac-neg 70.6%

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

   7. Simplified 70.6%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-207} \lor \neg \left(z \leq 2.05 \cdot 10^{-42}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 4: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-104} \lor \neg \left(y \leq 8.8 \cdot 10^{-98}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e-104) (not (<= y 8.8e-98))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e-104) || !(y <= 8.8e-98)) {
		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 <= (-5d-104)) .or. (.not. (y <= 8.8d-98))) 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 <= -5e-104) || !(y <= 8.8e-98)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e-104) or not (y <= 8.8e-98):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e-104) || !(y <= 8.8e-98))
		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 <= -5e-104) || ~((y <= 8.8e-98)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e-104], N[Not[LessEqual[y, 8.8e-98]], $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 < -4.99999999999999979e-104 or 8.79999999999999985e-98 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.6%

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

   if -4.99999999999999979e-104 < y < 8.79999999999999985e-98

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 90.6%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-104} \lor \neg \left(y \leq 8.8 \cdot 10^{-98}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 8.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 8.8e-11))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 8.8e-11)) {
		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 <= 8.8d-11))) 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 <= 8.8e-11)) {
		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 <= 8.8e-11):
		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 <= 8.8e-11))
		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 <= 8.8e-11)))
		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, 8.8e-11]], $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 8.8000000000000006e-11 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.5%

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

   if -1 < z < 8.8000000000000006e-11

   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 98.3%

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

      3. associate-+l- 98.3%

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

   3. Applied egg-rr 98.3%

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

   4. Taylor expanded in z around 0 96.6%

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

   5. Taylor expanded in y around 0 96.6%

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

      1. mul-1-neg 96.6%

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

      2. distribute-frac-neg 96.6%

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

      3. +-commutative 96.6%

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

      4. distribute-frac-neg 96.6%

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

      5. sub-neg 96.6%

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

      6. div-sub 98.4%

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

   7. Simplified 98.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 8.8 \cdot 10^{-11}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 6: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e+22) x (if (<= z 2.95e+47) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e+22) {
		tmp = x;
	} else if (z <= 2.95e+47) {
		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 <= (-1.15d+22)) then
        tmp = x
    else if (z <= 2.95d+47) 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 <= -1.15e+22) {
		tmp = x;
	} else if (z <= 2.95e+47) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e+22:
		tmp = x
	elif z <= 2.95e+47:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e+22)
		tmp = x;
	elseif (z <= 2.95e+47)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.15e+22)
		tmp = x;
	elseif (z <= 2.95e+47)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e+22], x, If[LessEqual[z, 2.95e+47], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1500000000000001e22 or 2.95000000000000017e47 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.1%

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

   if -1.1500000000000001e22 < z < 2.95000000000000017e47

   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 98.5%

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

      3. associate-+l- 98.5%

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

   3. Applied egg-rr 98.5%

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

   4. Taylor expanded in z around 0 92.7%

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

   5. Taylor expanded in y around inf 54.0%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 37.3% 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 41.9%

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

3. Final simplification 41.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))