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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 7

Speedup: 1.0×

• 21.1% 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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-271}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 490:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -3.4e-14)
     x
     (if (<= z -6.1e-58)
       (/ y z)
       (if (<= z -1.25e-101)
         t_0
         (if (<= z -9.5e-152)
           (/ y z)
           (if (<= z -2.25e-271)
             t_0
             (if (<= z 1.12e-290) (/ y z) (if (<= z 490.0) t_0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -3.4e-14) {
		tmp = x;
	} else if (z <= -6.1e-58) {
		tmp = y / z;
	} else if (z <= -1.25e-101) {
		tmp = t_0;
	} else if (z <= -9.5e-152) {
		tmp = y / z;
	} else if (z <= -2.25e-271) {
		tmp = t_0;
	} else if (z <= 1.12e-290) {
		tmp = y / z;
	} else if (z <= 490.0) {
		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 <= (-3.4d-14)) then
        tmp = x
    else if (z <= (-6.1d-58)) then
        tmp = y / z
    else if (z <= (-1.25d-101)) then
        tmp = t_0
    else if (z <= (-9.5d-152)) then
        tmp = y / z
    else if (z <= (-2.25d-271)) then
        tmp = t_0
    else if (z <= 1.12d-290) then
        tmp = y / z
    else if (z <= 490.0d0) 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 <= -3.4e-14) {
		tmp = x;
	} else if (z <= -6.1e-58) {
		tmp = y / z;
	} else if (z <= -1.25e-101) {
		tmp = t_0;
	} else if (z <= -9.5e-152) {
		tmp = y / z;
	} else if (z <= -2.25e-271) {
		tmp = t_0;
	} else if (z <= 1.12e-290) {
		tmp = y / z;
	} else if (z <= 490.0) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -3.4e-14:
		tmp = x
	elif z <= -6.1e-58:
		tmp = y / z
	elif z <= -1.25e-101:
		tmp = t_0
	elif z <= -9.5e-152:
		tmp = y / z
	elif z <= -2.25e-271:
		tmp = t_0
	elif z <= 1.12e-290:
		tmp = y / z
	elif z <= 490.0:
		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 <= -3.4e-14)
		tmp = x;
	elseif (z <= -6.1e-58)
		tmp = Float64(y / z);
	elseif (z <= -1.25e-101)
		tmp = t_0;
	elseif (z <= -9.5e-152)
		tmp = Float64(y / z);
	elseif (z <= -2.25e-271)
		tmp = t_0;
	elseif (z <= 1.12e-290)
		tmp = Float64(y / z);
	elseif (z <= 490.0)
		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 <= -3.4e-14)
		tmp = x;
	elseif (z <= -6.1e-58)
		tmp = y / z;
	elseif (z <= -1.25e-101)
		tmp = t_0;
	elseif (z <= -9.5e-152)
		tmp = y / z;
	elseif (z <= -2.25e-271)
		tmp = t_0;
	elseif (z <= 1.12e-290)
		tmp = y / z;
	elseif (z <= 490.0)
		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, -3.4e-14], x, If[LessEqual[z, -6.1e-58], N[(y / z), $MachinePrecision], If[LessEqual[z, -1.25e-101], t$95$0, If[LessEqual[z, -9.5e-152], N[(y / z), $MachinePrecision], If[LessEqual[z, -2.25e-271], t$95$0, If[LessEqual[z, 1.12e-290], N[(y / z), $MachinePrecision], If[LessEqual[z, 490.0], t$95$0, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000003e-14 or 490 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 72.5%

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

   if -3.40000000000000003e-14 < z < -6.1000000000000003e-58 or -1.25e-101 < z < -9.49999999999999925e-152 or -2.2499999999999999e-271 < z < 1.12e-290

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.5%

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

   3. Taylor expanded in x around 0 83.3%

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

   if -6.1000000000000003e-58 < z < -1.25e-101 or -9.49999999999999925e-152 < z < -2.2499999999999999e-271 or 1.12e-290 < z < 490

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 64.1%

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

   3. Taylor expanded in z around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. distribute-frac-neg 63.3%

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

   5. Simplified 63.3%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-101}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-152}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-271}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-290}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 490:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 86.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e+110)
   (- x (/ x z))
   (if (<= x 4.6e+64) (+ x (/ y z)) (* x (+ 1.0 (/ -1.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e+110) {
		tmp = x - (x / z);
	} else if (x <= 4.6e+64) {
		tmp = x + (y / z);
	} else {
		tmp = x * (1.0 + (-1.0 / 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 <= (-5.4d+110)) then
        tmp = x - (x / z)
    else if (x <= 4.6d+64) then
        tmp = x + (y / z)
    else
        tmp = x * (1.0d0 + ((-1.0d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e+110) {
		tmp = x - (x / z);
	} else if (x <= 4.6e+64) {
		tmp = x + (y / z);
	} else {
		tmp = x * (1.0 + (-1.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e+110:
		tmp = x - (x / z)
	elif x <= 4.6e+64:
		tmp = x + (y / z)
	else:
		tmp = x * (1.0 + (-1.0 / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e+110)
		tmp = Float64(x - Float64(x / z));
	elseif (x <= 4.6e+64)
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e+110)
		tmp = x - (x / z);
	elseif (x <= 4.6e+64)
		tmp = x + (y / z);
	else
		tmp = x * (1.0 + (-1.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e+110], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+64], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.40000000000000019e110

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.3%

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

   if -5.40000000000000019e110 < x < 4.6e64

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.9%

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

   if 4.6e64 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 94.8%

      \[\leadsto \color{blue}{\left(1 - \frac{1}{z}\right) \cdot x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+110}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z}\right)\\ \end{array} \]

Alternative 4: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-246} \lor \neg \left(y \leq -1.25 \cdot 10^{-288}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e-246) (not (<= y -1.25e-288))) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e-246) || !(y <= -1.25e-288)) {
		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 <= (-6.2d-246)) .or. (.not. (y <= (-1.25d-288)))) 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 <= -6.2e-246) || !(y <= -1.25e-288)) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.2e-246) or not (y <= -1.25e-288):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e-246) || !(y <= -1.25e-288))
		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 <= -6.2e-246) || ~((y <= -1.25e-288)))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e-246], N[Not[LessEqual[y, -1.25e-288]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.2000000000000001e-246 or -1.25000000000000003e-288 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.6%

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

   if -6.2000000000000001e-246 < y < -1.25000000000000003e-288

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.7%

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

   3. Taylor expanded in z around 0 76.3%

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

      1. mul-1-neg 76.3%

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

      2. distribute-frac-neg 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-246} \lor \neg \left(y \leq -1.25 \cdot 10^{-288}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \]

Alternative 5: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+112} \lor \neg \left(x \leq 1.8 \cdot 10^{+65}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2e+112) (not (<= x 1.8e+65))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2e+112) || !(x <= 1.8e+65)) {
		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 <= (-2d+112)) .or. (.not. (x <= 1.8d+65))) 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 <= -2e+112) || !(x <= 1.8e+65)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2e+112) or not (x <= 1.8e+65):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2e+112) || !(x <= 1.8e+65))
		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 <= -2e+112) || ~((x <= 1.8e+65)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2e+112], N[Not[LessEqual[x, 1.8e+65]], $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 < -1.9999999999999999e112 or 1.79999999999999989e65 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 91.5%

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

   if -1.9999999999999999e112 < x < 1.79999999999999989e65

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 90.9%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+112} \lor \neg \left(x \leq 1.8 \cdot 10^{+65}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 6: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2050:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.4e-14) x (if (<= z 2050.0) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.4e-14) {
		tmp = x;
	} else if (z <= 2050.0) {
		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 <= (-3.4d-14)) then
        tmp = x
    else if (z <= 2050.0d0) 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 <= -3.4e-14) {
		tmp = x;
	} else if (z <= 2050.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.4e-14:
		tmp = x
	elif z <= 2050.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.4e-14)
		tmp = x;
	elseif (z <= 2050.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.4e-14)
		tmp = x;
	elseif (z <= 2050.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.4e-14], x, If[LessEqual[z, 2050.0], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.40000000000000003e-14 or 2050 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 72.5%

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

   if -3.40000000000000003e-14 < z < 2050

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 55.3%

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

   3. Taylor expanded in x around 0 54.9%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2050:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 36.8% 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 38.3%

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

3. Final simplification 38.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))