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

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 7

Speedup: 1.0×

• 20.7% 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: 59.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-154}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-308}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-294}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -0.007)
     x
     (if (<= z -1.2e-69)
       (/ y z)
       (if (<= z -1.25e-154)
         t_0
         (if (<= z 3.4e-308)
           (/ y z)
           (if (<= z 3.8e-294)
             t_0
             (if (<= z 6.2e-217)
               (/ y z)
               (if (<= z 2.1e-23) t_0 (if (<= z 1.5e+150) (/ y z) x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -0.007) {
		tmp = x;
	} else if (z <= -1.2e-69) {
		tmp = y / z;
	} else if (z <= -1.25e-154) {
		tmp = t_0;
	} else if (z <= 3.4e-308) {
		tmp = y / z;
	} else if (z <= 3.8e-294) {
		tmp = t_0;
	} else if (z <= 6.2e-217) {
		tmp = y / z;
	} else if (z <= 2.1e-23) {
		tmp = t_0;
	} else if (z <= 1.5e+150) {
		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 <= (-0.007d0)) then
        tmp = x
    else if (z <= (-1.2d-69)) then
        tmp = y / z
    else if (z <= (-1.25d-154)) then
        tmp = t_0
    else if (z <= 3.4d-308) then
        tmp = y / z
    else if (z <= 3.8d-294) then
        tmp = t_0
    else if (z <= 6.2d-217) then
        tmp = y / z
    else if (z <= 2.1d-23) then
        tmp = t_0
    else if (z <= 1.5d+150) 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 <= -0.007) {
		tmp = x;
	} else if (z <= -1.2e-69) {
		tmp = y / z;
	} else if (z <= -1.25e-154) {
		tmp = t_0;
	} else if (z <= 3.4e-308) {
		tmp = y / z;
	} else if (z <= 3.8e-294) {
		tmp = t_0;
	} else if (z <= 6.2e-217) {
		tmp = y / z;
	} else if (z <= 2.1e-23) {
		tmp = t_0;
	} else if (z <= 1.5e+150) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -0.007:
		tmp = x
	elif z <= -1.2e-69:
		tmp = y / z
	elif z <= -1.25e-154:
		tmp = t_0
	elif z <= 3.4e-308:
		tmp = y / z
	elif z <= 3.8e-294:
		tmp = t_0
	elif z <= 6.2e-217:
		tmp = y / z
	elif z <= 2.1e-23:
		tmp = t_0
	elif z <= 1.5e+150:
		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 <= -0.007)
		tmp = x;
	elseif (z <= -1.2e-69)
		tmp = Float64(y / z);
	elseif (z <= -1.25e-154)
		tmp = t_0;
	elseif (z <= 3.4e-308)
		tmp = Float64(y / z);
	elseif (z <= 3.8e-294)
		tmp = t_0;
	elseif (z <= 6.2e-217)
		tmp = Float64(y / z);
	elseif (z <= 2.1e-23)
		tmp = t_0;
	elseif (z <= 1.5e+150)
		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 <= -0.007)
		tmp = x;
	elseif (z <= -1.2e-69)
		tmp = y / z;
	elseif (z <= -1.25e-154)
		tmp = t_0;
	elseif (z <= 3.4e-308)
		tmp = y / z;
	elseif (z <= 3.8e-294)
		tmp = t_0;
	elseif (z <= 6.2e-217)
		tmp = y / z;
	elseif (z <= 2.1e-23)
		tmp = t_0;
	elseif (z <= 1.5e+150)
		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, -0.007], x, If[LessEqual[z, -1.2e-69], N[(y / z), $MachinePrecision], If[LessEqual[z, -1.25e-154], t$95$0, If[LessEqual[z, 3.4e-308], N[(y / z), $MachinePrecision], If[LessEqual[z, 3.8e-294], t$95$0, If[LessEqual[z, 6.2e-217], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.1e-23], t$95$0, If[LessEqual[z, 1.5e+150], N[(y / z), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00700000000000000015 or 1.50000000000000006e150 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.3%

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

   if -0.00700000000000000015 < z < -1.2000000000000001e-69 or -1.25000000000000005e-154 < z < 3.39999999999999999e-308 or 3.8e-294 < z < 6.1999999999999997e-217 or 2.1000000000000001e-23 < z < 1.50000000000000006e150

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 65.4%

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

   if -1.2000000000000001e-69 < z < -1.25000000000000005e-154 or 3.39999999999999999e-308 < z < 3.8e-294 or 6.1999999999999997e-217 < z < 2.1000000000000001e-23

   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 70.8%

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

      1. neg-mul-1 70.8%

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

      2. distribute-neg-frac 70.8%

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

   5. Simplified 70.8%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-154}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-308}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-294}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-217}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-23}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 86.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+35} \lor \neg \left(y \leq 8.5 \cdot 10^{-107}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.1e+35) (not (<= y 8.5e-107))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.1e+35) || !(y <= 8.5e-107)) {
		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 <= (-2.1d+35)) .or. (.not. (y <= 8.5d-107))) 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 <= -2.1e+35) || !(y <= 8.5e-107)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.1e+35) or not (y <= 8.5e-107):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.1e+35) || !(y <= 8.5e-107))
		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 <= -2.1e+35) || ~((y <= 8.5e-107)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.1e+35], N[Not[LessEqual[y, 8.5e-107]], $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 < -2.0999999999999999e35 or 8.49999999999999956e-107 < y

   1. Initial program 99.9%

      \[x + \frac{y - x}{z} \]
   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 90.8%

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

   if -2.0999999999999999e35 < y < 8.49999999999999956e-107

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.8%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+35} \lor \neg \left(y \leq 8.5 \cdot 10^{-107}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 4: 98.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $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 1 < z

   1. Initial program 100.0%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 99.2%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 97.9%

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

4. Final simplification 98.5%

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

Alternative 5: 60.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.007) x (if (<= z 1.5e+150) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.007) {
		tmp = x;
	} else if (z <= 1.5e+150) {
		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 <= (-0.007d0)) then
        tmp = x
    else if (z <= 1.5d+150) 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 <= -0.007) {
		tmp = x;
	} else if (z <= 1.5e+150) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.007:
		tmp = x
	elif z <= 1.5e+150:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.007)
		tmp = x;
	elseif (z <= 1.5e+150)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.007)
		tmp = x;
	elseif (z <= 1.5e+150)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.007], x, If[LessEqual[z, 1.5e+150], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00700000000000000015 or 1.50000000000000006e150 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 81.3%

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

   if -0.00700000000000000015 < z < 1.50000000000000006e150

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 53.4%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+150}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -7.2e+124) (/ (- x) z) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -7.2e+124) {
		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 <= (-7.2d+124)) 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 <= -7.2e+124) {
		tmp = -x / z;
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -7.2e+124:
		tmp = -x / z
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -7.2e+124)
		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 <= -7.2e+124)
		tmp = -x / z;
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -7.2e+124], N[((-x) / z), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.19999999999999972e124

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 63.3%

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

   3. Taylor expanded in y around 0 57.3%

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

      1. neg-mul-1 57.3%

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

      2. distribute-neg-frac 57.3%

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

   5. Simplified 57.3%

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

   if -7.19999999999999972e124 < x

   1. Initial program 100.0%

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

      1. clear-num 99.6%

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

      2. inv-pow 99.6%

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

   3. Applied egg-rr 99.6%

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

   4. Taylor expanded in y around inf 80.5%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+124}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 7: 37.4% 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 37.5%

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

3. Final simplification 37.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))