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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

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: 61.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-28}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.7e+37)
   x
   (if (<= z 8.4e-88)
     (/ y z)
     (if (<= z 1.45e-28) (/ (- x) z) (if (<= z 3.6e+18) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.7e+37) {
		tmp = x;
	} else if (z <= 8.4e-88) {
		tmp = y / z;
	} else if (z <= 1.45e-28) {
		tmp = -x / z;
	} else if (z <= 3.6e+18) {
		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 <= (-3.7d+37)) then
        tmp = x
    else if (z <= 8.4d-88) then
        tmp = y / z
    else if (z <= 1.45d-28) then
        tmp = -x / z
    else if (z <= 3.6d+18) 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 <= -3.7e+37) {
		tmp = x;
	} else if (z <= 8.4e-88) {
		tmp = y / z;
	} else if (z <= 1.45e-28) {
		tmp = -x / z;
	} else if (z <= 3.6e+18) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.7e+37:
		tmp = x
	elif z <= 8.4e-88:
		tmp = y / z
	elif z <= 1.45e-28:
		tmp = -x / z
	elif z <= 3.6e+18:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.7e+37)
		tmp = x;
	elseif (z <= 8.4e-88)
		tmp = Float64(y / z);
	elseif (z <= 1.45e-28)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 3.6e+18)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.7e+37)
		tmp = x;
	elseif (z <= 8.4e-88)
		tmp = y / z;
	elseif (z <= 1.45e-28)
		tmp = -x / z;
	elseif (z <= 3.6e+18)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.7e+37], x, If[LessEqual[z, 8.4e-88], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.45e-28], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 3.6e+18], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6999999999999999e37 or 3.6e18 < 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 70.0%

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

   if -3.6999999999999999e37 < z < 8.3999999999999998e-88 or 1.45000000000000006e-28 < z < 3.6e18

   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 59.1

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

   5. Simplified 59.1%

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

   if 8.3999999999999998e-88 < z < 1.45000000000000006e-28

   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 100.0

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 77.8

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

   8. Simplified 77.8%

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

Alternative 3: 99.0% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))))
   (if (<= z -1.0) t_0 (if (<= z 1.0) (/ (- 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 <= 1.0) {
		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 <= 1.0d0) 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 <= 1.0) {
		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 <= 1.0:
		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 <= 1.0)
		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 <= 1.0)
		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, 1.0], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < 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 98.2

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

   5. Simplified 98.2%

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

   if -1 < z < 1

   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 98.6

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

   5. Simplified 98.6%

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

Alternative 4: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{z}\\ \mathbf{if}\;x \leq -9 \cdot 10^{+124}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9200000000:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x z))))
   (if (<= x -9e+124) t_0 (if (<= x 9200000000.0) (+ x (/ y z)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (x <= -9e+124) {
		tmp = t_0;
	} else if (x <= 9200000000.0) {
		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 <= (-9d+124)) then
        tmp = t_0
    else if (x <= 9200000000.0d0) 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 <= -9e+124) {
		tmp = t_0;
	} else if (x <= 9200000000.0) {
		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 <= -9e+124:
		tmp = t_0
	elif x <= 9200000000.0:
		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 <= -9e+124)
		tmp = t_0;
	elseif (x <= 9200000000.0)
		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 <= -9e+124)
		tmp = t_0;
	elseif (x <= 9200000000.0)
		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, -9e+124], t$95$0, If[LessEqual[x, 9200000000.0], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.0000000000000008e124 or 9.2e9 < 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 91.0

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

   5. Simplified 91.0%

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

   if -9.0000000000000008e124 < x < 9.2e9

   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 87.9

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

   5. Simplified 87.9%

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

Alternative 5: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-285}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-236}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))))
   (if (<= y -1.65e-285) t_0 (if (<= y 1.85e-236) (/ (- x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double tmp;
	if (y <= -1.65e-285) {
		tmp = t_0;
	} else if (y <= 1.85e-236) {
		tmp = -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 (y <= (-1.65d-285)) then
        tmp = t_0
    else if (y <= 1.85d-236) then
        tmp = -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 (y <= -1.65e-285) {
		tmp = t_0;
	} else if (y <= 1.85e-236) {
		tmp = -x / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / z)
	tmp = 0
	if y <= -1.65e-285:
		tmp = t_0
	elif y <= 1.85e-236:
		tmp = -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 (y <= -1.65e-285)
		tmp = t_0;
	elseif (y <= 1.85e-236)
		tmp = Float64(Float64(-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 (y <= -1.65e-285)
		tmp = t_0;
	elseif (y <= 1.85e-236)
		tmp = -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[y, -1.65e-285], t$95$0, If[LessEqual[y, 1.85e-236], N[((-x) / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.64999999999999993e-285 or 1.85000000000000011e-236 < y

   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 81.2

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

   5. Simplified 81.2%

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

   if -1.64999999999999993e-285 < y < 1.85000000000000011e-236

   1. Initial program 99.9%

      \[x + \frac{y - x}{z} \]
   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 94.2

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

   5. Simplified 94.2%

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

   6. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

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

      2. neg-lowering-neg.f64 89.1

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

   8. Simplified 89.1%

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

Alternative 6: 61.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.8e+37) x (if (<= z 5.4e+18) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.8e+37) {
		tmp = x;
	} else if (z <= 5.4e+18) {
		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 <= (-5.8d+37)) then
        tmp = x
    else if (z <= 5.4d+18) 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 <= -5.8e+37) {
		tmp = x;
	} else if (z <= 5.4e+18) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.8e+37:
		tmp = x
	elif z <= 5.4e+18:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.8e+37)
		tmp = x;
	elseif (z <= 5.4e+18)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.8e+37)
		tmp = x;
	elseif (z <= 5.4e+18)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.8e+37], x, If[LessEqual[z, 5.4e+18], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.79999999999999957e37 or 5.4e18 < 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 70.0%

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

   if -5.79999999999999957e37 < z < 5.4e18

   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 54.4

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

   5. Simplified 54.4%

      \[\leadsto \color{blue}{\frac{y}{z}} \]
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 34.3%

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

Reproduce

herbie shell --seed 2024204 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))