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

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 7

Speedup: 1.0×

• 21.4% 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: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-238}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-160}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.65e+70)
     x
     (if (<= z -2e-5)
       (/ y z)
       (if (<= z -6e-64)
         t_0
         (if (<= z -7.5e-88)
           (/ y z)
           (if (<= z 4.2e-238)
             t_0
             (if (<= z 3e-160) (/ y z) (if (<= z 1.0) t_0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.65e+70) {
		tmp = x;
	} else if (z <= -2e-5) {
		tmp = y / z;
	} else if (z <= -6e-64) {
		tmp = t_0;
	} else if (z <= -7.5e-88) {
		tmp = y / z;
	} else if (z <= 4.2e-238) {
		tmp = t_0;
	} else if (z <= 3e-160) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} 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 <= (-1.65d+70)) then
        tmp = x
    else if (z <= (-2d-5)) then
        tmp = y / z
    else if (z <= (-6d-64)) then
        tmp = t_0
    else if (z <= (-7.5d-88)) then
        tmp = y / z
    else if (z <= 4.2d-238) then
        tmp = t_0
    else if (z <= 3d-160) then
        tmp = y / z
    else if (z <= 1.0d0) then
        tmp = t_0
    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 <= -1.65e+70) {
		tmp = x;
	} else if (z <= -2e-5) {
		tmp = y / z;
	} else if (z <= -6e-64) {
		tmp = t_0;
	} else if (z <= -7.5e-88) {
		tmp = y / z;
	} else if (z <= 4.2e-238) {
		tmp = t_0;
	} else if (z <= 3e-160) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.65e+70:
		tmp = x
	elif z <= -2e-5:
		tmp = y / z
	elif z <= -6e-64:
		tmp = t_0
	elif z <= -7.5e-88:
		tmp = y / z
	elif z <= 4.2e-238:
		tmp = t_0
	elif z <= 3e-160:
		tmp = y / z
	elif z <= 1.0:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -1.65e+70)
		tmp = x;
	elseif (z <= -2e-5)
		tmp = Float64(y / z);
	elseif (z <= -6e-64)
		tmp = t_0;
	elseif (z <= -7.5e-88)
		tmp = Float64(y / z);
	elseif (z <= 4.2e-238)
		tmp = t_0;
	elseif (z <= 3e-160)
		tmp = Float64(y / z);
	elseif (z <= 1.0)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -1.65e+70)
		tmp = x;
	elseif (z <= -2e-5)
		tmp = y / z;
	elseif (z <= -6e-64)
		tmp = t_0;
	elseif (z <= -7.5e-88)
		tmp = y / z;
	elseif (z <= 4.2e-238)
		tmp = t_0;
	elseif (z <= 3e-160)
		tmp = y / z;
	elseif (z <= 1.0)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -1.65e+70], x, If[LessEqual[z, -2e-5], N[(y / z), $MachinePrecision], If[LessEqual[z, -6e-64], t$95$0, If[LessEqual[z, -7.5e-88], N[(y / z), $MachinePrecision], If[LessEqual[z, 4.2e-238], t$95$0, If[LessEqual[z, 3e-160], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$0, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.65000000000000008e70 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.6%

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

   if -1.65000000000000008e70 < z < -2.00000000000000016e-5 or -6.0000000000000001e-64 < z < -7.50000000000000041e-88 or 4.2000000000000002e-238 < z < 2.99999999999999997e-160

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 73.5%

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

   if -2.00000000000000016e-5 < z < -6.0000000000000001e-64 or -7.50000000000000041e-88 < z < 4.2000000000000002e-238 or 2.99999999999999997e-160 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.9%

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

   3. Taylor expanded in y around 0 68.2%

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

      1. neg-mul-1 68.2%

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

      2. distribute-neg-frac 68.2%

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

   5. Simplified 68.2%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-64}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-160}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-38}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-88}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-160}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ (- x) z)))
   (if (<= z -3.6e-38)
     t_0
     (if (<= z -6.5e-64)
       t_1
       (if (<= z -5.8e-88)
         t_0
         (if (<= z 1.8e-234)
           t_1
           (if (<= z 3.6e-160) (/ y z) (if (<= z 1.45e-45) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double t_1 = -x / z;
	double tmp;
	if (z <= -3.6e-38) {
		tmp = t_0;
	} else if (z <= -6.5e-64) {
		tmp = t_1;
	} else if (z <= -5.8e-88) {
		tmp = t_0;
	} else if (z <= 1.8e-234) {
		tmp = t_1;
	} else if (z <= 3.6e-160) {
		tmp = y / z;
	} else if (z <= 1.45e-45) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x + (y / z)
    t_1 = -x / z
    if (z <= (-3.6d-38)) then
        tmp = t_0
    else if (z <= (-6.5d-64)) then
        tmp = t_1
    else if (z <= (-5.8d-88)) then
        tmp = t_0
    else if (z <= 1.8d-234) then
        tmp = t_1
    else if (z <= 3.6d-160) then
        tmp = y / z
    else if (z <= 1.45d-45) then
        tmp = t_1
    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 t_1 = -x / z;
	double tmp;
	if (z <= -3.6e-38) {
		tmp = t_0;
	} else if (z <= -6.5e-64) {
		tmp = t_1;
	} else if (z <= -5.8e-88) {
		tmp = t_0;
	} else if (z <= 1.8e-234) {
		tmp = t_1;
	} else if (z <= 3.6e-160) {
		tmp = y / z;
	} else if (z <= 1.45e-45) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / z)
	t_1 = -x / z
	tmp = 0
	if z <= -3.6e-38:
		tmp = t_0
	elif z <= -6.5e-64:
		tmp = t_1
	elif z <= -5.8e-88:
		tmp = t_0
	elif z <= 1.8e-234:
		tmp = t_1
	elif z <= 3.6e-160:
		tmp = y / z
	elif z <= 1.45e-45:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y / z))
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -3.6e-38)
		tmp = t_0;
	elseif (z <= -6.5e-64)
		tmp = t_1;
	elseif (z <= -5.8e-88)
		tmp = t_0;
	elseif (z <= 1.8e-234)
		tmp = t_1;
	elseif (z <= 3.6e-160)
		tmp = Float64(y / z);
	elseif (z <= 1.45e-45)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y / z);
	t_1 = -x / z;
	tmp = 0.0;
	if (z <= -3.6e-38)
		tmp = t_0;
	elseif (z <= -6.5e-64)
		tmp = t_1;
	elseif (z <= -5.8e-88)
		tmp = t_0;
	elseif (z <= 1.8e-234)
		tmp = t_1;
	elseif (z <= 3.6e-160)
		tmp = y / z;
	elseif (z <= 1.45e-45)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -3.6e-38], t$95$0, If[LessEqual[z, -6.5e-64], t$95$1, If[LessEqual[z, -5.8e-88], t$95$0, If[LessEqual[z, 1.8e-234], t$95$1, If[LessEqual[z, 3.6e-160], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.45e-45], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6000000000000001e-38 or -6.5000000000000004e-64 < z < -5.8000000000000003e-88 or 1.45e-45 < 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. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 92.4%

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

   if -3.6000000000000001e-38 < z < -6.5000000000000004e-64 or -5.8000000000000003e-88 < z < 1.7999999999999999e-234 or 3.5999999999999997e-160 < z < 1.45e-45

   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 73.3%

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

      1. neg-mul-1 73.3%

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

      2. distribute-neg-frac 73.3%

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

   5. Simplified 73.3%

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

   if 1.7999999999999999e-234 < z < 3.5999999999999997e-160

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.2%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-88}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-234}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-160}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-45}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-61} \lor \neg \left(y \leq 5.7 \cdot 10^{+89}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.8e-61) (not (<= y 5.7e+89))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.8e-61) || !(y <= 5.7e+89)) {
		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 <= (-2.8d-61)) .or. (.not. (y <= 5.7d+89))) 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 <= -2.8e-61) || !(y <= 5.7e+89)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.8e-61) or not (y <= 5.7e+89):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.8e-61) || !(y <= 5.7e+89))
		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 <= -2.8e-61) || ~((y <= 5.7e+89)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.8e-61], N[Not[LessEqual[y, 5.7e+89]], $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 < -2.8000000000000001e-61 or 5.6999999999999995e89 < y

   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. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 88.9%

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

   if -2.8000000000000001e-61 < y < 5.6999999999999995e89

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 86.5%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-61} \lor \neg \left(y \leq 5.7 \cdot 10^{+89}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 5: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+28} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2e+28) (not (<= z 1.0))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2e+28) || !(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 <= (-2d+28)) .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 <= -2e+28) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2e+28) 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 <= -2e+28) || !(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 <= -2e+28) || ~((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, -2e+28], 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 < -1.99999999999999992e28 or 1 < 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. associate-/r/ 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around inf 100.0%

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

   if -1.99999999999999992e28 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 97.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+28} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 6: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1600000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6e+69) x (if (<= z 1600000.0) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6e+69) {
		tmp = x;
	} else if (z <= 1600000.0) {
		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 <= (-6d+69)) then
        tmp = x
    else if (z <= 1600000.0d0) 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 <= -6e+69) {
		tmp = x;
	} else if (z <= 1600000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6e+69:
		tmp = x
	elif z <= 1600000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6e+69)
		tmp = x;
	elseif (z <= 1600000.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6e+69)
		tmp = x;
	elseif (z <= 1600000.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6e+69], x, If[LessEqual[z, 1600000.0], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.99999999999999967e69 or 1.6e6 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.6%

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

   if -5.99999999999999967e69 < z < 1.6e6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 47.6%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1600000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 35.2%

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

3. Final simplification 35.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023257 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))