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

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 6

Speedup: 1.0×

• 21.2% 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: 60.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -31:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-199}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-122}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -31.0)
     x
     (if (<= z 2.6e-199)
       (/ y z)
       (if (<= z 1.12e-122)
         t_0
         (if (<= z 5.5e-83)
           (/ y z)
           (if (<= z 3.5e-31) t_0 (if (<= z 3.9e+58) (/ y z) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -31.0) {
		tmp = x;
	} else if (z <= 2.6e-199) {
		tmp = y / z;
	} else if (z <= 1.12e-122) {
		tmp = t_0;
	} else if (z <= 5.5e-83) {
		tmp = y / z;
	} else if (z <= 3.5e-31) {
		tmp = t_0;
	} else if (z <= 3.9e+58) {
		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 <= (-31.0d0)) then
        tmp = x
    else if (z <= 2.6d-199) then
        tmp = y / z
    else if (z <= 1.12d-122) then
        tmp = t_0
    else if (z <= 5.5d-83) then
        tmp = y / z
    else if (z <= 3.5d-31) then
        tmp = t_0
    else if (z <= 3.9d+58) 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 <= -31.0) {
		tmp = x;
	} else if (z <= 2.6e-199) {
		tmp = y / z;
	} else if (z <= 1.12e-122) {
		tmp = t_0;
	} else if (z <= 5.5e-83) {
		tmp = y / z;
	} else if (z <= 3.5e-31) {
		tmp = t_0;
	} else if (z <= 3.9e+58) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -31.0:
		tmp = x
	elif z <= 2.6e-199:
		tmp = y / z
	elif z <= 1.12e-122:
		tmp = t_0
	elif z <= 5.5e-83:
		tmp = y / z
	elif z <= 3.5e-31:
		tmp = t_0
	elif z <= 3.9e+58:
		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 <= -31.0)
		tmp = x;
	elseif (z <= 2.6e-199)
		tmp = Float64(y / z);
	elseif (z <= 1.12e-122)
		tmp = t_0;
	elseif (z <= 5.5e-83)
		tmp = Float64(y / z);
	elseif (z <= 3.5e-31)
		tmp = t_0;
	elseif (z <= 3.9e+58)
		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 <= -31.0)
		tmp = x;
	elseif (z <= 2.6e-199)
		tmp = y / z;
	elseif (z <= 1.12e-122)
		tmp = t_0;
	elseif (z <= 5.5e-83)
		tmp = y / z;
	elseif (z <= 3.5e-31)
		tmp = t_0;
	elseif (z <= 3.9e+58)
		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, -31.0], x, If[LessEqual[z, 2.6e-199], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.12e-122], t$95$0, If[LessEqual[z, 5.5e-83], N[(y / z), $MachinePrecision], If[LessEqual[z, 3.5e-31], t$95$0, If[LessEqual[z, 3.9e+58], N[(y / z), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -31 or 3.9000000000000001e58 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 75.0%

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

   if -31 < z < 2.6000000000000001e-199 or 1.12e-122 < z < 5.49999999999999964e-83 or 3.49999999999999985e-31 < z < 3.9000000000000001e58

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 64.6%

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

   if 2.6000000000000001e-199 < z < 1.12e-122 or 5.49999999999999964e-83 < z < 3.49999999999999985e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. sub-neg 78.3%

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

      2. distribute-neg-frac 78.3%

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

      3. metadata-eval 78.3%

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

      4. metadata-eval 78.3%

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

      5. associate-/r* 78.3%

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

      6. neg-mul-1 78.3%

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

      7. distribute-lft-out 78.3%

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

      8. *-rgt-identity 78.3%

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

      9. associate-*r/ 78.6%

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

      10. neg-mul-1 78.6%

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

      11. *-commutative 78.6%

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

      12. times-frac 78.6%

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

      13. metadata-eval 78.6%

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

      14. *-commutative 78.6%

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

      15. neg-mul-1 78.6%

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

      16. sub-neg 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. distribute-frac-neg 78.6%

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

   7. Simplified 78.6%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-199}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-122}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+58}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-120} \lor \neg \left(x \leq 2.8 \cdot 10^{+26}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.5e-120) (not (<= x 2.8e+26))) (- x (/ x z)) (/ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-120) || !(x <= 2.8e+26)) {
		tmp = x - (x / z);
	} else {
		tmp = 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 <= (-3.5d-120)) .or. (.not. (x <= 2.8d+26))) then
        tmp = x - (x / z)
    else
        tmp = y / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.5e-120) || !(x <= 2.8e+26)) {
		tmp = x - (x / z);
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.5e-120) or not (x <= 2.8e+26):
		tmp = x - (x / z)
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.5e-120) || !(x <= 2.8e+26))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(y / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3.5e-120) || ~((x <= 2.8e+26)))
		tmp = x - (x / z);
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.5e-120], N[Not[LessEqual[x, 2.8e+26]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e-120 or 2.8e26 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 82.7%

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

      1. sub-neg 82.7%

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

      2. distribute-neg-frac 82.7%

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

      3. metadata-eval 82.7%

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

      4. metadata-eval 82.7%

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

      5. associate-/r* 82.7%

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

      6. neg-mul-1 82.7%

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

      7. distribute-lft-out 82.7%

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

      8. *-rgt-identity 82.7%

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

      9. associate-*r/ 82.8%

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

      10. neg-mul-1 82.8%

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

      11. *-commutative 82.8%

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

      12. times-frac 82.8%

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

      13. metadata-eval 82.8%

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

      14. *-commutative 82.8%

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

      15. neg-mul-1 82.8%

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

      16. sub-neg 82.8%

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

   4. Simplified 82.8%

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

   if -3.5e-120 < x < 2.8e26

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-120} \lor \neg \left(x \leq 2.8 \cdot 10^{+26}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \]

Alternative 4: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.45) (- x (/ x z)) (if (<= z 8.5e+58) (/ (- y x) z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.45) {
		tmp = x - (x / z);
	} else if (z <= 8.5e+58) {
		tmp = (y - x) / 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 <= (-0.45d0)) then
        tmp = x - (x / z)
    else if (z <= 8.5d+58) then
        tmp = (y - x) / 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 <= -0.45) {
		tmp = x - (x / z);
	} else if (z <= 8.5e+58) {
		tmp = (y - x) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.45:
		tmp = x - (x / z)
	elif z <= 8.5e+58:
		tmp = (y - x) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.45)
		tmp = Float64(x - Float64(x / z));
	elseif (z <= 8.5e+58)
		tmp = Float64(Float64(y - x) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.45)
		tmp = x - (x / z);
	elseif (z <= 8.5e+58)
		tmp = (y - x) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.45], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.5e+58], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -0.450000000000000011

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.2%

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

      1. sub-neg 75.2%

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

      2. distribute-neg-frac 75.2%

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

      3. metadata-eval 75.2%

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

      4. metadata-eval 75.2%

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

      5. associate-/r* 75.2%

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

      6. neg-mul-1 75.2%

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

      7. distribute-lft-out 75.2%

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

      8. *-rgt-identity 75.2%

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

      9. associate-*r/ 75.2%

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

      10. neg-mul-1 75.2%

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

      11. *-commutative 75.2%

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

      12. times-frac 75.2%

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

      13. metadata-eval 75.2%

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

      14. *-commutative 75.2%

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

      15. neg-mul-1 75.2%

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

      16. sub-neg 75.2%

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

   4. Simplified 75.2%

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

   if -0.450000000000000011 < z < 8.50000000000000015e58

   1. Initial program 100.0%

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

   2. Taylor expanded in z around 0 95.4%

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

   if 8.50000000000000015e58 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 76.1%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -31:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -31.0) x (if (<= z 3.6e+60) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -31.0) {
		tmp = x;
	} else if (z <= 3.6e+60) {
		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 <= (-31.0d0)) then
        tmp = x
    else if (z <= 3.6d+60) 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 <= -31.0) {
		tmp = x;
	} else if (z <= 3.6e+60) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -31.0:
		tmp = x
	elif z <= 3.6e+60:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -31.0)
		tmp = x;
	elseif (z <= 3.6e+60)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -31.0)
		tmp = x;
	elseif (z <= 3.6e+60)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -31.0], x, If[LessEqual[z, 3.6e+60], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -31 or 3.59999999999999968e60 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 75.0%

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

   if -31 < z < 3.59999999999999968e60

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 58.2%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -31:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+60}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 36.2% 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 38.0%

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

3. Final simplification 38.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))