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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

Alternatives: 7

Speedup: 1.0×

• 21.5% 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: 62.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.06 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-298}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.00055:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.06e+20)
     x
     (if (<= z -1.2e-299)
       (/ y z)
       (if (<= z 2.7e-298)
         t_0
         (if (<= z 8.5e-100)
           (/ y z)
           (if (<= z 0.00055) t_0 (if (<= z 2.35e+29) (/ y z) x))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.06e+20) {
		tmp = x;
	} else if (z <= -1.2e-299) {
		tmp = y / z;
	} else if (z <= 2.7e-298) {
		tmp = t_0;
	} else if (z <= 8.5e-100) {
		tmp = y / z;
	} else if (z <= 0.00055) {
		tmp = t_0;
	} else if (z <= 2.35e+29) {
		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 <= (-1.06d+20)) then
        tmp = x
    else if (z <= (-1.2d-299)) then
        tmp = y / z
    else if (z <= 2.7d-298) then
        tmp = t_0
    else if (z <= 8.5d-100) then
        tmp = y / z
    else if (z <= 0.00055d0) then
        tmp = t_0
    else if (z <= 2.35d+29) 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 <= -1.06e+20) {
		tmp = x;
	} else if (z <= -1.2e-299) {
		tmp = y / z;
	} else if (z <= 2.7e-298) {
		tmp = t_0;
	} else if (z <= 8.5e-100) {
		tmp = y / z;
	} else if (z <= 0.00055) {
		tmp = t_0;
	} else if (z <= 2.35e+29) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.06e+20:
		tmp = x
	elif z <= -1.2e-299:
		tmp = y / z
	elif z <= 2.7e-298:
		tmp = t_0
	elif z <= 8.5e-100:
		tmp = y / z
	elif z <= 0.00055:
		tmp = t_0
	elif z <= 2.35e+29:
		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 <= -1.06e+20)
		tmp = x;
	elseif (z <= -1.2e-299)
		tmp = Float64(y / z);
	elseif (z <= 2.7e-298)
		tmp = t_0;
	elseif (z <= 8.5e-100)
		tmp = Float64(y / z);
	elseif (z <= 0.00055)
		tmp = t_0;
	elseif (z <= 2.35e+29)
		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 <= -1.06e+20)
		tmp = x;
	elseif (z <= -1.2e-299)
		tmp = y / z;
	elseif (z <= 2.7e-298)
		tmp = t_0;
	elseif (z <= 8.5e-100)
		tmp = y / z;
	elseif (z <= 0.00055)
		tmp = t_0;
	elseif (z <= 2.35e+29)
		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, -1.06e+20], x, If[LessEqual[z, -1.2e-299], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.7e-298], t$95$0, If[LessEqual[z, 8.5e-100], N[(y / z), $MachinePrecision], If[LessEqual[z, 0.00055], t$95$0, If[LessEqual[z, 2.35e+29], N[(y / z), $MachinePrecision], x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.06e20 or 2.3500000000000001e29 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 71.4%

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

   if -1.06e20 < z < -1.2000000000000001e-299 or 2.7000000000000001e-298 < z < 8.50000000000000017e-100 or 5.50000000000000033e-4 < z < 2.3500000000000001e29

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 67.9%

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

   if -1.2000000000000001e-299 < z < 2.7000000000000001e-298 or 8.50000000000000017e-100 < z < 5.50000000000000033e-4

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 92.3%

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

   3. Taylor expanded in y around 0 68.5%

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

      1. neg-mul-1 68.5%

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

      2. distribute-neg-frac 68.5%

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

   5. Simplified 68.5%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.06 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-299}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-298}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.00055:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{-209} \lor \neg \left(y \leq 1.05 \cdot 10^{-189} \lor \neg \left(y \leq 1.5 \cdot 10^{-138}\right) \land y \leq 8.1 \cdot 10^{-115}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y 4.2e-209)
         (not
          (or (<= y 1.05e-189) (and (not (<= y 1.5e-138)) (<= y 8.1e-115)))))
   (+ x (/ y z))
   (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= 4.2e-209) || !((y <= 1.05e-189) || (!(y <= 1.5e-138) && (y <= 8.1e-115)))) {
		tmp = x + (y / z);
	} else {
		tmp = -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 <= 4.2d-209) .or. (.not. (y <= 1.05d-189) .or. (.not. (y <= 1.5d-138)) .and. (y <= 8.1d-115))) then
        tmp = x + (y / z)
    else
        tmp = -x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= 4.2e-209) || !((y <= 1.05e-189) || (!(y <= 1.5e-138) && (y <= 8.1e-115)))) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= 4.2e-209) or not ((y <= 1.05e-189) or (not (y <= 1.5e-138) and (y <= 8.1e-115))):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= 4.2e-209) || !((y <= 1.05e-189) || (!(y <= 1.5e-138) && (y <= 8.1e-115))))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= 4.2e-209) || ~(((y <= 1.05e-189) || (~((y <= 1.5e-138)) && (y <= 8.1e-115)))))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, 4.2e-209], N[Not[Or[LessEqual[y, 1.05e-189], And[N[Not[LessEqual[y, 1.5e-138]], $MachinePrecision], LessEqual[y, 8.1e-115]]]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.19999999999999991e-209 or 1.05000000000000008e-189 < y < 1.5e-138 or 8.0999999999999999e-115 < 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. 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 82.4%

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

   if 4.19999999999999991e-209 < y < 1.05000000000000008e-189 or 1.5e-138 < y < 8.0999999999999999e-115

   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 0 100.0%

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

      1. neg-mul-1 100.0%

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

      2. distribute-neg-frac 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.2 \cdot 10^{-209} \lor \neg \left(y \leq 1.05 \cdot 10^{-189} \lor \neg \left(y \leq 1.5 \cdot 10^{-138}\right) \land y \leq 8.1 \cdot 10^{-115}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-60} \lor \neg \left(y \leq 6.5 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.2e-60) (not (<= y 6.5e-85))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.2e-60) || !(y <= 6.5e-85)) {
		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 <= (-4.2d-60)) .or. (.not. (y <= 6.5d-85))) 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 <= -4.2e-60) || !(y <= 6.5e-85)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.2e-60) or not (y <= 6.5e-85):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.2e-60) || !(y <= 6.5e-85))
		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 <= -4.2e-60) || ~((y <= 6.5e-85)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -4.2e-60], N[Not[LessEqual[y, 6.5e-85]], $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 < -4.19999999999999982e-60 or 6.5e-85 < 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. 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 90.0%

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

   if -4.19999999999999982e-60 < y < 6.5e-85

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 85.9%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-60} \lor \neg \left(y \leq 6.5 \cdot 10^{-85}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 5: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.00135\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.00135))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.00135)) {
		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 <= 0.00135d0))) 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 <= 0.00135)) {
		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 <= 0.00135):
		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 <= 0.00135))
		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 <= 0.00135)))
		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, 0.00135]], $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 0.0013500000000000001 < z

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

   3. Applied egg-rr 99.9%

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

   4. Taylor expanded in y around inf 99.2%

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

   if -1 < z < 0.0013500000000000001

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.00135\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]

Alternative 6: 62.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.2e+20) x (if (<= z 2.9e+30) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.2e+20) {
		tmp = x;
	} else if (z <= 2.9e+30) {
		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 <= (-2.2d+20)) then
        tmp = x
    else if (z <= 2.9d+30) 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 <= -2.2e+20) {
		tmp = x;
	} else if (z <= 2.9e+30) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.2e+20:
		tmp = x
	elif z <= 2.9e+30:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.2e+20)
		tmp = x;
	elseif (z <= 2.9e+30)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.2e+20)
		tmp = x;
	elseif (z <= 2.9e+30)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.2e+20], x, If[LessEqual[z, 2.9e+30], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2e20 or 2.8999999999999998e30 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 71.4%

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

   if -2.2e20 < z < 2.8999999999999998e30

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 60.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 37.0% 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 33.1%

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

3. Final simplification 33.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))