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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 7

Speedup: 1.0×

• 20.4% 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: 61.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-246}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -2e+25)
     x
     (if (<= z -5e-62)
       (/ y z)
       (if (<= z -4.2e-190)
         t_0
         (if (<= z -3.4e-246)
           (/ y z)
           (if (<= z 8.8e-222)
             t_0
             (if (<= z 4.5e-89) (/ 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 <= -2e+25) {
		tmp = x;
	} else if (z <= -5e-62) {
		tmp = y / z;
	} else if (z <= -4.2e-190) {
		tmp = t_0;
	} else if (z <= -3.4e-246) {
		tmp = y / z;
	} else if (z <= 8.8e-222) {
		tmp = t_0;
	} else if (z <= 4.5e-89) {
		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 <= (-2d+25)) then
        tmp = x
    else if (z <= (-5d-62)) then
        tmp = y / z
    else if (z <= (-4.2d-190)) then
        tmp = t_0
    else if (z <= (-3.4d-246)) then
        tmp = y / z
    else if (z <= 8.8d-222) then
        tmp = t_0
    else if (z <= 4.5d-89) 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 <= -2e+25) {
		tmp = x;
	} else if (z <= -5e-62) {
		tmp = y / z;
	} else if (z <= -4.2e-190) {
		tmp = t_0;
	} else if (z <= -3.4e-246) {
		tmp = y / z;
	} else if (z <= 8.8e-222) {
		tmp = t_0;
	} else if (z <= 4.5e-89) {
		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 <= -2e+25:
		tmp = x
	elif z <= -5e-62:
		tmp = y / z
	elif z <= -4.2e-190:
		tmp = t_0
	elif z <= -3.4e-246:
		tmp = y / z
	elif z <= 8.8e-222:
		tmp = t_0
	elif z <= 4.5e-89:
		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 <= -2e+25)
		tmp = x;
	elseif (z <= -5e-62)
		tmp = Float64(y / z);
	elseif (z <= -4.2e-190)
		tmp = t_0;
	elseif (z <= -3.4e-246)
		tmp = Float64(y / z);
	elseif (z <= 8.8e-222)
		tmp = t_0;
	elseif (z <= 4.5e-89)
		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 <= -2e+25)
		tmp = x;
	elseif (z <= -5e-62)
		tmp = y / z;
	elseif (z <= -4.2e-190)
		tmp = t_0;
	elseif (z <= -3.4e-246)
		tmp = y / z;
	elseif (z <= 8.8e-222)
		tmp = t_0;
	elseif (z <= 4.5e-89)
		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, -2e+25], x, If[LessEqual[z, -5e-62], N[(y / z), $MachinePrecision], If[LessEqual[z, -4.2e-190], t$95$0, If[LessEqual[z, -3.4e-246], N[(y / z), $MachinePrecision], If[LessEqual[z, 8.8e-222], t$95$0, If[LessEqual[z, 4.5e-89], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$0, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.00000000000000018e25 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 74.2%

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

   if -2.00000000000000018e25 < z < -5.0000000000000002e-62 or -4.19999999999999983e-190 < z < -3.4000000000000001e-246 or 8.8000000000000001e-222 < z < 4.4999999999999999e-89

   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 96.0%

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

      3. associate-+l- 96.0%

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

   3. Applied egg-rr 96.0%

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

   4. Taylor expanded in y around inf 63.2%

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

   if -5.0000000000000002e-62 < z < -4.19999999999999983e-190 or -3.4000000000000001e-246 < z < 8.8000000000000001e-222 or 4.4999999999999999e-89 < z < 1

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 68.7%

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

   3. Taylor expanded in z around 0 68.5%

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

      1. mul-1-neg 68.5%

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

      2. distribute-frac-neg 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 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-190}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-246}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-245}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ (- x) z)))
   (if (<= z -3.5e-61)
     t_0
     (if (<= z -4.8e-188)
       t_1
       (if (<= z -2.2e-245)
         (/ y z)
         (if (<= z 7.6e-227)
           t_1
           (if (<= z 7e-89) (/ y z) (if (<= z 4.7e-36) 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 <= -3.5e-61) {
		tmp = t_0;
	} else if (z <= -4.8e-188) {
		tmp = t_1;
	} else if (z <= -2.2e-245) {
		tmp = y / z;
	} else if (z <= 7.6e-227) {
		tmp = t_1;
	} else if (z <= 7e-89) {
		tmp = y / z;
	} else if (z <= 4.7e-36) {
		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 <= (-3.5d-61)) then
        tmp = t_0
    else if (z <= (-4.8d-188)) then
        tmp = t_1
    else if (z <= (-2.2d-245)) then
        tmp = y / z
    else if (z <= 7.6d-227) then
        tmp = t_1
    else if (z <= 7d-89) then
        tmp = y / z
    else if (z <= 4.7d-36) 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 <= -3.5e-61) {
		tmp = t_0;
	} else if (z <= -4.8e-188) {
		tmp = t_1;
	} else if (z <= -2.2e-245) {
		tmp = y / z;
	} else if (z <= 7.6e-227) {
		tmp = t_1;
	} else if (z <= 7e-89) {
		tmp = y / z;
	} else if (z <= 4.7e-36) {
		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 <= -3.5e-61:
		tmp = t_0
	elif z <= -4.8e-188:
		tmp = t_1
	elif z <= -2.2e-245:
		tmp = y / z
	elif z <= 7.6e-227:
		tmp = t_1
	elif z <= 7e-89:
		tmp = y / z
	elif z <= 4.7e-36:
		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 <= -3.5e-61)
		tmp = t_0;
	elseif (z <= -4.8e-188)
		tmp = t_1;
	elseif (z <= -2.2e-245)
		tmp = Float64(y / z);
	elseif (z <= 7.6e-227)
		tmp = t_1;
	elseif (z <= 7e-89)
		tmp = Float64(y / z);
	elseif (z <= 4.7e-36)
		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 <= -3.5e-61)
		tmp = t_0;
	elseif (z <= -4.8e-188)
		tmp = t_1;
	elseif (z <= -2.2e-245)
		tmp = y / z;
	elseif (z <= 7.6e-227)
		tmp = t_1;
	elseif (z <= 7e-89)
		tmp = y / z;
	elseif (z <= 4.7e-36)
		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, -3.5e-61], t$95$0, If[LessEqual[z, -4.8e-188], t$95$1, If[LessEqual[z, -2.2e-245], N[(y / z), $MachinePrecision], If[LessEqual[z, 7.6e-227], t$95$1, If[LessEqual[z, 7e-89], N[(y / z), $MachinePrecision], If[LessEqual[z, 4.7e-36], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5000000000000003e-61 or 4.7000000000000003e-36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.5%

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

   if -3.5000000000000003e-61 < z < -4.8e-188 or -2.19999999999999993e-245 < z < 7.60000000000000019e-227 or 6.9999999999999994e-89 < z < 4.7000000000000003e-36

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 70.9%

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

   3. Taylor expanded in z around 0 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-frac-neg 71.1%

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

   5. Simplified 71.1%

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

   if -4.8e-188 < z < -2.19999999999999993e-245 or 7.60000000000000019e-227 < z < 6.9999999999999994e-89

   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 93.7%

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

      3. associate-+l- 93.7%

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

   3. Applied egg-rr 93.7%

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

   4. Taylor expanded in y around inf 66.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-61}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-188}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-245}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-227}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-89}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-36}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-63} \lor \neg \left(y \leq 4.6 \cdot 10^{-13}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.2e-63) (not (<= y 4.6e-13))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.2e-63) || !(y <= 4.6e-13)) {
		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 <= (-9.2d-63)) .or. (.not. (y <= 4.6d-13))) 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 <= -9.2e-63) || !(y <= 4.6e-13)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.2e-63) or not (y <= 4.6e-13):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.2e-63) || !(y <= 4.6e-13))
		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 <= -9.2e-63) || ~((y <= 4.6e-13)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.2e-63], N[Not[LessEqual[y, 4.6e-13]], $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 < -9.2e-63 or 4.59999999999999958e-13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 89.1%

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

   if -9.2e-63 < y < 4.59999999999999958e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 89.4%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-63} \lor \neg \left(y \leq 4.6 \cdot 10^{-13}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 5: 98.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) 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 <= -1.0) || !(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 <= -1.0) || ~((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, -1.0], 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 < -1 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.1%

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

   if -1 < z < 1

   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 95.6%

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

      3. associate-+l- 95.6%

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

   3. Applied egg-rr 95.6%

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

   4. Taylor expanded in z around 0 98.8%

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

4. Final simplification 98.4%

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

Alternative 6: 62.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.8e+23) x (if (<= z 3e+44) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.8e+23) {
		tmp = x;
	} else if (z <= 3e+44) {
		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 <= (-3.8d+23)) then
        tmp = x
    else if (z <= 3d+44) 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 <= -3.8e+23) {
		tmp = x;
	} else if (z <= 3e+44) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.8e+23:
		tmp = x
	elif z <= 3e+44:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.8e+23)
		tmp = x;
	elseif (z <= 3e+44)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.8e+23)
		tmp = x;
	elseif (z <= 3e+44)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.8e+23], x, If[LessEqual[z, 3e+44], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999975e23 or 2.99999999999999987e44 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 77.4%

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

   if -3.79999999999999975e23 < z < 2.99999999999999987e44

   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 96.2%

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

      3. associate-+l- 96.2%

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

   3. Applied egg-rr 96.2%

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

   4. Taylor expanded in y around inf 48.5%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+44}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 37.1% 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 41.0%

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

3. Final simplification 41.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))