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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 7

Speedup: 1.0×

• 20.2% 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: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{-271}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.7e+126)
     x
     (if (<= z -3.4e+90)
       (/ y z)
       (if (<= z -4.1e+49)
         x
         (if (<= z -1.1e-236)
           (/ y z)
           (if (<= z 1e-271)
             t_0
             (if (<= z 1.55e-143)
               (/ y z)
               (if (<= z 1.75e-127) t_0 (if (<= z 4.6e+26) (/ y z) x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.7e+126) {
		tmp = x;
	} else if (z <= -3.4e+90) {
		tmp = y / z;
	} else if (z <= -4.1e+49) {
		tmp = x;
	} else if (z <= -1.1e-236) {
		tmp = y / z;
	} else if (z <= 1e-271) {
		tmp = t_0;
	} else if (z <= 1.55e-143) {
		tmp = y / z;
	} else if (z <= 1.75e-127) {
		tmp = t_0;
	} else if (z <= 4.6e+26) {
		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 <= (-1.7d+126)) then
        tmp = x
    else if (z <= (-3.4d+90)) then
        tmp = y / z
    else if (z <= (-4.1d+49)) then
        tmp = x
    else if (z <= (-1.1d-236)) then
        tmp = y / z
    else if (z <= 1d-271) then
        tmp = t_0
    else if (z <= 1.55d-143) then
        tmp = y / z
    else if (z <= 1.75d-127) then
        tmp = t_0
    else if (z <= 4.6d+26) 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 <= -1.7e+126) {
		tmp = x;
	} else if (z <= -3.4e+90) {
		tmp = y / z;
	} else if (z <= -4.1e+49) {
		tmp = x;
	} else if (z <= -1.1e-236) {
		tmp = y / z;
	} else if (z <= 1e-271) {
		tmp = t_0;
	} else if (z <= 1.55e-143) {
		tmp = y / z;
	} else if (z <= 1.75e-127) {
		tmp = t_0;
	} else if (z <= 4.6e+26) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.7e+126:
		tmp = x
	elif z <= -3.4e+90:
		tmp = y / z
	elif z <= -4.1e+49:
		tmp = x
	elif z <= -1.1e-236:
		tmp = y / z
	elif z <= 1e-271:
		tmp = t_0
	elif z <= 1.55e-143:
		tmp = y / z
	elif z <= 1.75e-127:
		tmp = t_0
	elif z <= 4.6e+26:
		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 <= -1.7e+126)
		tmp = x;
	elseif (z <= -3.4e+90)
		tmp = Float64(y / z);
	elseif (z <= -4.1e+49)
		tmp = x;
	elseif (z <= -1.1e-236)
		tmp = Float64(y / z);
	elseif (z <= 1e-271)
		tmp = t_0;
	elseif (z <= 1.55e-143)
		tmp = Float64(y / z);
	elseif (z <= 1.75e-127)
		tmp = t_0;
	elseif (z <= 4.6e+26)
		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 <= -1.7e+126)
		tmp = x;
	elseif (z <= -3.4e+90)
		tmp = y / z;
	elseif (z <= -4.1e+49)
		tmp = x;
	elseif (z <= -1.1e-236)
		tmp = y / z;
	elseif (z <= 1e-271)
		tmp = t_0;
	elseif (z <= 1.55e-143)
		tmp = y / z;
	elseif (z <= 1.75e-127)
		tmp = t_0;
	elseif (z <= 4.6e+26)
		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, -1.7e+126], x, If[LessEqual[z, -3.4e+90], N[(y / z), $MachinePrecision], If[LessEqual[z, -4.1e+49], x, If[LessEqual[z, -1.1e-236], N[(y / z), $MachinePrecision], If[LessEqual[z, 1e-271], t$95$0, If[LessEqual[z, 1.55e-143], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.75e-127], t$95$0, If[LessEqual[z, 4.6e+26], N[(y / z), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.69999999999999995e126 or -3.40000000000000018e90 < z < -4.1e49 or 4.6000000000000001e26 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 79.9%

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

   if -1.69999999999999995e126 < z < -3.40000000000000018e90 or -4.1e49 < z < -1.09999999999999996e-236 or 9.99999999999999963e-272 < z < 1.55000000000000004e-143 or 1.74999999999999995e-127 < z < 4.6000000000000001e26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 62.0%

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

   if -1.09999999999999996e-236 < z < 9.99999999999999963e-272 or 1.55000000000000004e-143 < z < 1.74999999999999995e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.3%

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

   3. Taylor expanded in z around 0 78.3%

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

      1. mul-1-neg 78.3%

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

      2. distribute-frac-neg 78.3%

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

   5. Simplified 78.3%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{+49}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-236}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 10^{-271}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-127}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 60.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e+126)
   x
   (if (<= z -3.4e+90)
     (/ y z)
     (if (<= z -2.75e+45) x (if (<= z 4.8e+26) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+126) {
		tmp = x;
	} else if (z <= -3.4e+90) {
		tmp = y / z;
	} else if (z <= -2.75e+45) {
		tmp = x;
	} else if (z <= 4.8e+26) {
		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 <= (-1.8d+126)) then
        tmp = x
    else if (z <= (-3.4d+90)) then
        tmp = y / z
    else if (z <= (-2.75d+45)) then
        tmp = x
    else if (z <= 4.8d+26) 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 <= -1.8e+126) {
		tmp = x;
	} else if (z <= -3.4e+90) {
		tmp = y / z;
	} else if (z <= -2.75e+45) {
		tmp = x;
	} else if (z <= 4.8e+26) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e+126:
		tmp = x
	elif z <= -3.4e+90:
		tmp = y / z
	elif z <= -2.75e+45:
		tmp = x
	elif z <= 4.8e+26:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e+126)
		tmp = x;
	elseif (z <= -3.4e+90)
		tmp = Float64(y / z);
	elseif (z <= -2.75e+45)
		tmp = x;
	elseif (z <= 4.8e+26)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e+126)
		tmp = x;
	elseif (z <= -3.4e+90)
		tmp = y / z;
	elseif (z <= -2.75e+45)
		tmp = x;
	elseif (z <= 4.8e+26)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e+126], x, If[LessEqual[z, -3.4e+90], N[(y / z), $MachinePrecision], If[LessEqual[z, -2.75e+45], x, If[LessEqual[z, 4.8e+26], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e126 or -3.40000000000000018e90 < z < -2.75e45 or 4.80000000000000009e26 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 79.9%

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

   if -1.8e126 < z < -3.40000000000000018e90 or -2.75e45 < z < 4.80000000000000009e26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 56.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+26}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+31} \lor \neg \left(x \leq 5.1 \cdot 10^{+135}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+31) (not (<= x 5.1e+135))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+31) || !(x <= 5.1e+135)) {
		tmp = x - (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 <= (-9.5d+31)) .or. (.not. (x <= 5.1d+135))) then
        tmp = x - (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 <= -9.5e+31) || !(x <= 5.1e+135)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e+31) or not (x <= 5.1e+135):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e+31) || !(x <= 5.1e+135))
		tmp = Float64(x - 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 <= -9.5e+31) || ~((x <= 5.1e+135)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e+31], N[Not[LessEqual[x, 5.1e+135]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000008e31 or 5.09999999999999982e135 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.8%

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

   if -9.5000000000000008e31 < x < 5.09999999999999982e135

   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 inf 87.1%

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

      1. neg-mul-1 87.1%

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

   6. Simplified 87.1%

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

   7. Taylor expanded in y around 0 87.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+31} \lor \neg \left(x \leq 5.1 \cdot 10^{+135}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 5: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -34000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -34000000000.0) (not (<= z 1.0))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -34000000000.0) || !(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 <= (-34000000000.0d0)) .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 <= -34000000000.0) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -34000000000.0) 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 <= -34000000000.0) || !(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 <= -34000000000.0) || ~((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, -34000000000.0], 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 < -3.4e10 or 1 < z

   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 inf 99.2%

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

      1. neg-mul-1 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in y around 0 99.2%

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

   if -3.4e10 < z < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 99.1%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -34000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 6: 75.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ y z)))

C

double code(double x, double y, double z) {
	return x + (y / 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 / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (y / z);
}

Python

def code(x, y, z):
	return x + (y / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(y / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (y / z);
end

Wolfram

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

Derivation

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 inf 77.5%

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

   1. neg-mul-1 77.5%

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

6. Simplified 77.5%

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

7. Taylor expanded in y around 0 77.5%

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

8. Final simplification 77.5%

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

Alternative 7: 36.5% 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 38.4%

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

3. Final simplification 38.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))