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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 7

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 76.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y - x}{z} \leq -\infty:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (+ x (/ (- y x) z)) (- INFINITY)) (- (/ x z)) (+ x (/ y z))))

C

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

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x + ((y - x) / z)) <= -Double.POSITIVE_INFINITY) {
		tmp = -(x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x + ((y - x) / z)) <= -math.inf:
		tmp = -(x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y - x) / z)) <= Float64(-Inf))
		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 + ((y - x) / z)) <= -Inf)
		tmp = -(x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (-.f64 y x) z)) < -inf.0

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. distribute-lft-out-- N/A

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

      2. *-rgt-identity N/A

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

      3. associate-*r/ N/A

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

      4. *-rgt-identity N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 71.5

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

   5. Simplified 71.5%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x}{z}\right)} \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \color{blue}{\frac{x}{\mathsf{neg}\left(z\right)}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{\mathsf{neg}\left(z\right)}} \]

      4. neg-lowering-neg.f64 71.5

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

   8. Simplified 71.5%

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

   if -inf.0 < (+.f64 x (/.f64 (-.f64 y x) z))

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 80.9

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

   5. Simplified 80.9%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y - x}{z} \leq -\infty:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{-274}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -195.0)
   x
   (if (<= z -3.25e-80)
     (/ y z)
     (if (<= z 1e-274) (- (/ x z)) (if (<= z 2.3e+107) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -195.0) {
		tmp = x;
	} else if (z <= -3.25e-80) {
		tmp = y / z;
	} else if (z <= 1e-274) {
		tmp = -(x / z);
	} else if (z <= 2.3e+107) {
		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 <= (-195.0d0)) then
        tmp = x
    else if (z <= (-3.25d-80)) then
        tmp = y / z
    else if (z <= 1d-274) then
        tmp = -(x / z)
    else if (z <= 2.3d+107) 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 <= -195.0) {
		tmp = x;
	} else if (z <= -3.25e-80) {
		tmp = y / z;
	} else if (z <= 1e-274) {
		tmp = -(x / z);
	} else if (z <= 2.3e+107) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -195.0:
		tmp = x
	elif z <= -3.25e-80:
		tmp = y / z
	elif z <= 1e-274:
		tmp = -(x / z)
	elif z <= 2.3e+107:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -195.0)
		tmp = x;
	elseif (z <= -3.25e-80)
		tmp = Float64(y / z);
	elseif (z <= 1e-274)
		tmp = Float64(-Float64(x / z));
	elseif (z <= 2.3e+107)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -195.0)
		tmp = x;
	elseif (z <= -3.25e-80)
		tmp = y / z;
	elseif (z <= 1e-274)
		tmp = -(x / z);
	elseif (z <= 2.3e+107)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -195.0], x, If[LessEqual[z, -3.25e-80], N[(y / z), $MachinePrecision], If[LessEqual[z, 1e-274], (-N[(x / z), $MachinePrecision]), If[LessEqual[z, 2.3e+107], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -195 or 2.3e107 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Simplified 82.1%

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

   if -195 < z < -3.24999999999999992e-80 or 9.99999999999999966e-275 < z < 2.3e107

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 58.3

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

   5. Simplified 58.3%

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

   if -3.24999999999999992e-80 < z < 9.99999999999999966e-275

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. distribute-lft-out-- N/A

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

      2. *-rgt-identity N/A

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

      3. associate-*r/ N/A

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

      4. *-rgt-identity N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 59.8

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(\frac{x}{z}\right)} \]

      2. distribute-neg-frac2 N/A

         \[\leadsto \color{blue}{\frac{x}{\mathsf{neg}\left(z\right)}} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \color{blue}{\frac{x}{\mathsf{neg}\left(z\right)}} \]

      4. neg-lowering-neg.f64 59.8

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

   8. Simplified 59.8%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -195:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.25 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{-274}:\\ \;\;\;\;-\frac{x}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.000175:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))))
   (if (<= z -1.0) t_0 (if (<= z 0.000175) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 0.000175) {
		tmp = (y - x) / z;
	} else {
		tmp = t_0;
	}
	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 + (y / z)
    if (z <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 0.000175d0) then
        tmp = (y - x) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 0.000175) {
		tmp = (y - x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / z)
	tmp = 0
	if z <= -1.0:
		tmp = t_0
	elif z <= 0.000175:
		tmp = (y - x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y / z))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 0.000175)
		tmp = Float64(Float64(y - x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y / z);
	tmp = 0.0;
	if (z <= -1.0)
		tmp = t_0;
	elseif (z <= 0.000175)
		tmp = (y - x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$0, If[LessEqual[z, 0.000175], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.74999999999999998e-4 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 97.7

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

   5. Simplified 97.7%

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

   if -1 < z < 1.74999999999999998e-4

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

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

      1. /-lowering-/.f64 N/A

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

      2. --lowering--.f64 99.4

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

   5. Simplified 99.4%

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

Alternative 5: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{z}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-50}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x z))))
   (if (<= x -2.15e+73) t_0 (if (<= x 5.6e-50) (+ x (/ y z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (x <= -2.15e+73) {
		tmp = t_0;
	} else if (x <= 5.6e-50) {
		tmp = x + (y / z);
	} else {
		tmp = t_0;
	}
	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 - (x / z)
    if (x <= (-2.15d+73)) then
        tmp = t_0
    else if (x <= 5.6d-50) then
        tmp = x + (y / z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (x <= -2.15e+73) {
		tmp = t_0;
	} else if (x <= 5.6e-50) {
		tmp = x + (y / z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (x / z)
	tmp = 0
	if x <= -2.15e+73:
		tmp = t_0
	elif x <= 5.6e-50:
		tmp = x + (y / z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(x / z))
	tmp = 0.0
	if (x <= -2.15e+73)
		tmp = t_0;
	elseif (x <= 5.6e-50)
		tmp = Float64(x + Float64(y / z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (x / z);
	tmp = 0.0;
	if (x <= -2.15e+73)
		tmp = t_0;
	elseif (x <= 5.6e-50)
		tmp = x + (y / z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.15e+73], t$95$0, If[LessEqual[x, 5.6e-50], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.15000000000000007e73 or 5.5999999999999996e-50 < x

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. distribute-lft-out-- N/A

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

      2. *-rgt-identity N/A

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

      3. associate-*r/ N/A

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

      4. *-rgt-identity N/A

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

      5. --lowering--.f64 N/A

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

      6. /-lowering-/.f64 93.8

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

   5. Simplified 93.8%

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

   if -2.15000000000000007e73 < x < 5.5999999999999996e-50

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

      1. /-lowering-/.f64 87.8

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

   5. Simplified 87.8%

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

Alternative 6: 60.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -195:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -195.0) x (if (<= z 4.2e+107) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -195.0) {
		tmp = x;
	} else if (z <= 4.2e+107) {
		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 <= (-195.0d0)) then
        tmp = x
    else if (z <= 4.2d+107) 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 <= -195.0) {
		tmp = x;
	} else if (z <= 4.2e+107) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -195.0:
		tmp = x
	elif z <= 4.2e+107:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -195.0)
		tmp = x;
	elseif (z <= 4.2e+107)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -195.0)
		tmp = x;
	elseif (z <= 4.2e+107)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -195.0], x, If[LessEqual[z, 4.2e+107], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -195 or 4.1999999999999999e107 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

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

   5. Simplified 82.1%

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

   if -195 < z < 4.1999999999999999e107

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 52.8

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

   5. Simplified 52.8%

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

Alternative 7: 36.9% accurate, 18.0× 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. Add Preprocessing

3. Taylor expanded in z around inf

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

5. Simplified 41.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024199 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))