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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 54.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{-z}\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+114}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z))))
   (if (<= x -7.8e+114)
     t_0
     (if (<= x -9.6e-5)
       x
       (if (<= x 8.6e+23) (/ y z) (if (<= x 3.2e+143) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x / -z;
	double tmp;
	if (x <= -7.8e+114) {
		tmp = t_0;
	} else if (x <= -9.6e-5) {
		tmp = x;
	} else if (x <= 8.6e+23) {
		tmp = y / z;
	} else if (x <= 3.2e+143) {
		tmp = x;
	} 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) :: tmp
    t_0 = x / -z
    if (x <= (-7.8d+114)) then
        tmp = t_0
    else if (x <= (-9.6d-5)) then
        tmp = x
    else if (x <= 8.6d+23) then
        tmp = y / z
    else if (x <= 3.2d+143) then
        tmp = x
    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 / -z;
	double tmp;
	if (x <= -7.8e+114) {
		tmp = t_0;
	} else if (x <= -9.6e-5) {
		tmp = x;
	} else if (x <= 8.6e+23) {
		tmp = y / z;
	} else if (x <= 3.2e+143) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / -z
	tmp = 0
	if x <= -7.8e+114:
		tmp = t_0
	elif x <= -9.6e-5:
		tmp = x
	elif x <= 8.6e+23:
		tmp = y / z
	elif x <= 3.2e+143:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(-z))
	tmp = 0.0
	if (x <= -7.8e+114)
		tmp = t_0;
	elseif (x <= -9.6e-5)
		tmp = x;
	elseif (x <= 8.6e+23)
		tmp = Float64(y / z);
	elseif (x <= 3.2e+143)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / -z;
	tmp = 0.0;
	if (x <= -7.8e+114)
		tmp = t_0;
	elseif (x <= -9.6e-5)
		tmp = x;
	elseif (x <= 8.6e+23)
		tmp = y / z;
	elseif (x <= 3.2e+143)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / (-z)), $MachinePrecision]}, If[LessEqual[x, -7.8e+114], t$95$0, If[LessEqual[x, -9.6e-5], x, If[LessEqual[x, 8.6e+23], N[(y / z), $MachinePrecision], If[LessEqual[x, 3.2e+143], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.8000000000000001e114 or 3.20000000000000016e143 < x

   1. Initial program 100.0%

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

      1. div-sub 92.1%

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

      2. sub-neg 92.1%

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

      3. distribute-frac-neg 92.1%

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

      4. +-commutative 92.1%

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

      5. associate-+r+ 92.1%

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

      6. distribute-frac-neg 92.1%

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

      7. sub-neg 92.1%

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

      8. associate--r- 92.1%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 94.8%

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

      1. distribute-lft-out-- 94.7%

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

      2. *-rgt-identity 94.7%

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

      3. associate-*r/ 94.8%

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

      4. *-rgt-identity 94.8%

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

   7. Simplified 94.8%

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

   8. Taylor expanded in z around 0 61.7%

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

      1. mul-1-neg 61.7%

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

      2. distribute-frac-neg 61.7%

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

   10. Simplified 61.7%

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

   if -7.8000000000000001e114 < x < -9.6000000000000002e-5 or 8.5999999999999997e23 < x < 3.20000000000000016e143

   1. Initial program 100.0%

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

      1. div-sub 98.0%

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

      2. sub-neg 98.0%

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

      3. distribute-frac-neg 98.0%

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

      4. +-commutative 98.0%

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

      5. associate-+r+ 98.0%

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

      6. distribute-frac-neg 98.0%

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

      7. sub-neg 98.0%

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

      8. associate--r- 98.0%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 54.3%

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

   if -9.6000000000000002e-5 < x < 8.5999999999999997e23

   1. Initial program 100.0%

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

      1. div-sub 99.2%

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

      2. sub-neg 99.2%

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

      3. distribute-frac-neg 99.2%

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

      4. +-commutative 99.2%

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

      5. associate-+r+ 99.2%

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

      6. distribute-frac-neg 99.2%

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

      7. sub-neg 99.2%

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

      8. associate--r- 99.2%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 75.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+114}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.7 \cdot 10^{-9}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.7e-9))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.7e-9)) {
		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 <= 1.7d-9))) 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 <= 1.7e-9)) {
		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 <= 1.7e-9):
		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 <= 1.7e-9))
		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 <= 1.7e-9)))
		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, 1.7e-9]], $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 1.6999999999999999e-9 < z

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r- 100.0%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 98.5%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.5%

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

   8. Taylor expanded in x around 0 98.5%

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

      1. cancel-sign-sub-inv 98.5%

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

      2. metadata-eval 98.5%

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

      3. *-lft-identity 98.5%

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

      4. +-commutative 98.5%

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

   10. Simplified 98.5%

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

   if -1 < z < 1.6999999999999999e-9

   1. Initial program 100.0%

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

      1. div-sub 94.1%

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

      2. sub-neg 94.1%

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

      3. distribute-frac-neg 94.1%

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

      4. +-commutative 94.1%

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

      5. associate-+r+ 94.1%

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

      6. distribute-frac-neg 94.1%

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

      7. sub-neg 94.1%

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

      8. associate--r- 94.1%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 99.1%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.7 \cdot 10^{-9}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00122 \lor \neg \left(x \leq 3.9 \cdot 10^{+115}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -0.00122) (not (<= x 3.9e+115))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -0.00122) || !(x <= 3.9e+115)) {
		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 <= (-0.00122d0)) .or. (.not. (x <= 3.9d+115))) 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 <= -0.00122) || !(x <= 3.9e+115)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -0.00122) or not (x <= 3.9e+115):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -0.00122) || !(x <= 3.9e+115))
		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 <= -0.00122) || ~((x <= 3.9e+115)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -0.00122], N[Not[LessEqual[x, 3.9e+115]], $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 < -0.00121999999999999995 or 3.90000000000000006e115 < x

   1. Initial program 100.0%

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

      1. div-sub 93.4%

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

      2. sub-neg 93.4%

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

      3. distribute-frac-neg 93.4%

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

      4. +-commutative 93.4%

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

      5. associate-+r+ 93.4%

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

      6. distribute-frac-neg 93.4%

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

      7. sub-neg 93.4%

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

      8. associate--r- 93.4%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 92.5%

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

      1. distribute-lft-out-- 92.5%

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

      2. *-rgt-identity 92.5%

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

      3. associate-*r/ 92.6%

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

      4. *-rgt-identity 92.6%

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

   7. Simplified 92.6%

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

   if -0.00121999999999999995 < x < 3.90000000000000006e115

   1. Initial program 100.0%

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

      1. div-sub 99.3%

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

      2. sub-neg 99.3%

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

      3. distribute-frac-neg 99.3%

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

      4. +-commutative 99.3%

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

      5. associate-+r+ 99.3%

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

      6. distribute-frac-neg 99.3%

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

      7. sub-neg 99.3%

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

      8. associate--r- 99.3%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 92.5%

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

      1. neg-mul-1 92.5%

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

   7. Simplified 92.5%

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

   8. Taylor expanded in x around 0 92.5%

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

      1. cancel-sign-sub-inv 92.5%

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

      2. metadata-eval 92.5%

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

      3. *-lft-identity 92.5%

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

      4. +-commutative 92.5%

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

   10. Simplified 92.5%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00122 \lor \neg \left(x \leq 3.9 \cdot 10^{+115}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+164} \lor \neg \left(x \leq 2 \cdot 10^{+145}\right):\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.02e+164) (not (<= x 2e+145))) (/ x (- z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e+164) || !(x <= 2e+145)) {
		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 <= (-1.02d+164)) .or. (.not. (x <= 2d+145))) 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 <= -1.02e+164) || !(x <= 2e+145)) {
		tmp = x / -z;
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.02e+164) or not (x <= 2e+145):
		tmp = x / -z
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.02e+164) || !(x <= 2e+145))
		tmp = Float64(x / Float64(-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 <= -1.02e+164) || ~((x <= 2e+145)))
		tmp = x / -z;
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.02e+164], N[Not[LessEqual[x, 2e+145]], $MachinePrecision]], N[(x / (-z)), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e164 or 2e145 < x

   1. Initial program 100.0%

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

      1. div-sub 92.4%

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

      2. sub-neg 92.4%

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

      3. distribute-frac-neg 92.4%

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

      4. +-commutative 92.4%

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

      5. associate-+r+ 92.4%

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

      6. distribute-frac-neg 92.4%

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

      7. sub-neg 92.4%

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

      8. associate--r- 92.4%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 96.9%

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

      1. distribute-lft-out-- 96.9%

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

      2. *-rgt-identity 96.9%

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

      3. associate-*r/ 96.9%

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

      4. *-rgt-identity 96.9%

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

   7. Simplified 96.9%

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

   8. Taylor expanded in z around 0 63.2%

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

      1. mul-1-neg 63.2%

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

      2. distribute-frac-neg 63.2%

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

   10. Simplified 63.2%

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

   if -1.02e164 < x < 2e145

   1. Initial program 100.0%

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

      1. div-sub 98.4%

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

      2. sub-neg 98.4%

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

      3. distribute-frac-neg 98.4%

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

      4. +-commutative 98.4%

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

      5. associate-+r+ 98.4%

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

      6. distribute-frac-neg 98.4%

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

      7. sub-neg 98.4%

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

      8. associate--r- 98.4%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 86.5%

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

      1. neg-mul-1 86.5%

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

   7. Simplified 86.5%

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

   8. Taylor expanded in x around 0 86.5%

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

      1. cancel-sign-sub-inv 86.5%

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

      2. metadata-eval 86.5%

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

      3. *-lft-identity 86.5%

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

      4. +-commutative 86.5%

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

   10. Simplified 86.5%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+164} \lor \neg \left(x \leq 2 \cdot 10^{+145}\right):\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+70}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8e+18) x (if (<= z 1.85e+70) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8e+18) {
		tmp = x;
	} else if (z <= 1.85e+70) {
		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 <= (-8d+18)) then
        tmp = x
    else if (z <= 1.85d+70) 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 <= -8e+18) {
		tmp = x;
	} else if (z <= 1.85e+70) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8e+18:
		tmp = x
	elif z <= 1.85e+70:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8e+18)
		tmp = x;
	elseif (z <= 1.85e+70)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8e+18)
		tmp = x;
	elseif (z <= 1.85e+70)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8e+18], x, If[LessEqual[z, 1.85e+70], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8e18 or 1.84999999999999994e70 < z

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. distribute-frac-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. associate-+r+ 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. sub-neg 100.0%

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

      8. associate--r- 100.0%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 70.4%

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

   if -8e18 < z < 1.84999999999999994e70

   1. Initial program 100.0%

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

      1. div-sub 94.9%

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

      2. sub-neg 94.9%

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

      3. distribute-frac-neg 94.9%

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

      4. +-commutative 94.9%

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

      5. associate-+r+ 94.9%

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

      6. distribute-frac-neg 94.9%

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

      7. sub-neg 94.9%

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

      8. associate--r- 94.9%

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

      9. div-sub 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 55.2%

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

Alternative 7: 36.7% 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. div-sub 96.9%

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

   2. sub-neg 96.9%

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

   3. distribute-frac-neg 96.9%

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

   4. +-commutative 96.9%

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

   5. associate-+r+ 96.9%

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

   6. distribute-frac-neg 96.9%

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

   7. sub-neg 96.9%

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

   8. associate--r- 96.9%

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

   9. div-sub 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{x - \frac{x - y}{z}} \]
4. Add Preprocessing

5. Taylor expanded in z around inf 31.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))