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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 7

Speedup: 1.0×

• 20.9% 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: 62.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -6.4e+35)
     x
     (if (<= z 2.3e-187)
       (/ y z)
       (if (<= z 2.95e-40)
         t_0
         (if (<= z 2.6e-18) (/ 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 <= -6.4e+35) {
		tmp = x;
	} else if (z <= 2.3e-187) {
		tmp = y / z;
	} else if (z <= 2.95e-40) {
		tmp = t_0;
	} else if (z <= 2.6e-18) {
		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 <= (-6.4d+35)) then
        tmp = x
    else if (z <= 2.3d-187) then
        tmp = y / z
    else if (z <= 2.95d-40) then
        tmp = t_0
    else if (z <= 2.6d-18) 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 <= -6.4e+35) {
		tmp = x;
	} else if (z <= 2.3e-187) {
		tmp = y / z;
	} else if (z <= 2.95e-40) {
		tmp = t_0;
	} else if (z <= 2.6e-18) {
		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 <= -6.4e+35:
		tmp = x
	elif z <= 2.3e-187:
		tmp = y / z
	elif z <= 2.95e-40:
		tmp = t_0
	elif z <= 2.6e-18:
		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 <= -6.4e+35)
		tmp = x;
	elseif (z <= 2.3e-187)
		tmp = Float64(y / z);
	elseif (z <= 2.95e-40)
		tmp = t_0;
	elseif (z <= 2.6e-18)
		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 <= -6.4e+35)
		tmp = x;
	elseif (z <= 2.3e-187)
		tmp = y / z;
	elseif (z <= 2.95e-40)
		tmp = t_0;
	elseif (z <= 2.6e-18)
		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, -6.4e+35], x, If[LessEqual[z, 2.3e-187], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.95e-40], t$95$0, If[LessEqual[z, 2.6e-18], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$0, x]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.39999999999999965e35 or 1 < z

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 77.6%

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

   if -6.39999999999999965e35 < z < 2.29999999999999998e-187 or 2.94999999999999983e-40 < z < 2.6e-18

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. neg-sub0 99.9%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 99.9%

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

      4. remove-double-neg 99.9%

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

      5. --rgt-identity 99.9%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 99.9%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 99.9%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 99.9%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 99.9%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 57.6%

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

   if 2.29999999999999998e-187 < z < 2.94999999999999983e-40 or 2.6e-18 < z < 1

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 71.4%

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

   5. Taylor expanded in z around 0 69.7%

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

      1. mul-1-neg 69.7%

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

      2. distribute-frac-neg 69.7%

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

   7. Simplified 69.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+35}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-187}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-40}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-21} \lor \neg \left(y \leq 2.85 \cdot 10^{-30}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.4e-21) (not (<= y 2.85e-30))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.4e-21) || !(y <= 2.85e-30)) {
		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 <= (-5.4d-21)) .or. (.not. (y <= 2.85d-30))) 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 <= -5.4e-21) || !(y <= 2.85e-30)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.4e-21) or not (y <= 2.85e-30):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.4e-21) || !(y <= 2.85e-30))
		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 <= -5.4e-21) || ~((y <= 2.85e-30)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.4e-21], N[Not[LessEqual[y, 2.85e-30]], $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 < -5.4000000000000002e-21 or 2.84999999999999989e-30 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 87.8%

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

      1. neg-mul-1 87.8%

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

      2. distribute-neg-frac 87.8%

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

   6. Simplified 87.8%

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

      1. sub-neg 87.8%

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

      2. distribute-frac-neg 87.8%

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

      3. remove-double-neg 87.8%

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

      4. +-commutative 87.8%

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

   8. Applied egg-rr 87.8%

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

   if -5.4000000000000002e-21 < y < 2.84999999999999989e-30

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 90.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-21} \lor \neg \left(y \leq 2.85 \cdot 10^{-30}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \]

Alternative 4: 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. Step-by-step derivation

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 98.8%

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

      1. neg-mul-1 98.8%

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

      2. distribute-neg-frac 98.8%

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

   6. Simplified 98.8%

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

      1. sub-neg 98.8%

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

      2. distribute-frac-neg 98.8%

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

      3. remove-double-neg 98.8%

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

      4. +-commutative 98.8%

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

   8. Applied egg-rr 98.8%

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

   if -1 < z < 1

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. neg-sub0 99.9%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 99.9%

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

      4. remove-double-neg 99.9%

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

      5. --rgt-identity 99.9%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 99.9%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 99.9%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 99.9%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 99.9%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around 0 99.0%

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

4. Final simplification 98.9%

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

Alternative 5: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1600000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.9e+34) x (if (<= z 1600000.0) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.9e+34) {
		tmp = x;
	} else if (z <= 1600000.0) {
		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 <= (-1.9d+34)) then
        tmp = x
    else if (z <= 1600000.0d0) 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 <= -1.9e+34) {
		tmp = x;
	} else if (z <= 1600000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.9e+34:
		tmp = x
	elif z <= 1600000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.9e+34)
		tmp = x;
	elseif (z <= 1600000.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.9e+34)
		tmp = x;
	elseif (z <= 1600000.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.9e+34], x, If[LessEqual[z, 1600000.0], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000001e34 or 1.6e6 < z

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 78.2%

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

   if -1.9000000000000001e34 < z < 1.6e6

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. neg-sub0 99.9%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 99.9%

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

      4. remove-double-neg 99.9%

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

      5. --rgt-identity 99.9%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 99.9%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 99.9%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 99.9%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 99.9%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 50.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1600000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+238}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.22e+238) (/ (- x) z) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.22e+238) {
		tmp = -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 <= (-1.22d+238)) then
        tmp = -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 <= -1.22e+238) {
		tmp = -x / z;
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.22e+238:
		tmp = -x / z
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.22e+238)
		tmp = Float64(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 <= -1.22e+238)
		tmp = -x / z;
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.22e+238], N[((-x) / z), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2200000000000001e238

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. neg-sub0 99.9%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 99.9%

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

      4. remove-double-neg 99.9%

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

      5. --rgt-identity 99.9%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 99.9%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 99.9%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 99.9%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 99.9%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 99.9%

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

      11. +-commutative 99.9%

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

      12. sub-neg 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 99.9%

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

   5. Taylor expanded in z around 0 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-frac-neg 75.0%

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

   7. Simplified 75.0%

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

   if -1.2200000000000001e238 < x

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. neg-sub0 100.0%

         \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

      3. neg-sub0 100.0%

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

      4. remove-double-neg 100.0%

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

      5. --rgt-identity 100.0%

         \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

      6. associate-+l- 100.0%

         \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

      7. div0 100.0%

         \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

      8. div-sub 100.0%

         \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

      9. associate-+l- 100.0%

         \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

      10. neg-sub0 100.0%

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

      11. +-commutative 100.0%

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

      12. sub-neg 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 76.8%

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

      1. neg-mul-1 76.8%

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

      2. distribute-neg-frac 76.8%

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

   6. Simplified 76.8%

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

      1. sub-neg 76.8%

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

      2. distribute-frac-neg 76.8%

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

      3. remove-double-neg 76.8%

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

      4. +-commutative 76.8%

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

   8. Applied egg-rr 76.8%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+238}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 7: 37.2% 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. Step-by-step derivation

   1. remove-double-neg 100.0%

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

   2. neg-sub0 100.0%

      \[\leadsto \color{blue}{\left(0 - \left(-x\right)\right)} + \frac{y - x}{z} \]

   3. neg-sub0 100.0%

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

   4. remove-double-neg 100.0%

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

   5. --rgt-identity 100.0%

      \[\leadsto \color{blue}{\left(x - 0\right)} + \frac{y - x}{z} \]

   6. associate-+l- 100.0%

      \[\leadsto \color{blue}{x - \left(0 - \frac{y - x}{z}\right)} \]

   7. div0 100.0%

      \[\leadsto x - \left(\color{blue}{\frac{0}{z}} - \frac{y - x}{z}\right) \]

   8. div-sub 100.0%

      \[\leadsto x - \color{blue}{\frac{0 - \left(y - x\right)}{z}} \]

   9. associate-+l- 100.0%

      \[\leadsto x - \frac{\color{blue}{\left(0 - y\right) + x}}{z} \]

   10. neg-sub0 100.0%

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

   11. +-commutative 100.0%

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

   12. sub-neg 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in z around inf 39.5%

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

5. Final simplification 39.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))