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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

Alternatives: 7

Speedup: 1.0×

• 20.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - x}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (/ (- y x) z)))

C

double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) / z)
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) / z);
}

Python

def code(x, y, z):
	return x + ((y - x) / z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) / z);
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 60.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{-z}\\ \mathbf{if}\;z \leq -4 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-245}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-198}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 470000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ x (- z))))
   (if (<= z -4e+89)
     x
     (if (<= z -5.4e-41)
       (/ y z)
       (if (<= z -4.8e-83)
         t_0
         (if (<= z -1.85e-102)
           (/ y z)
           (if (<= z -4.6e-245)
             t_0
             (if (<= z 3.8e-198)
               (/ y z)
               (if (<= z 1.7e-19)
                 t_0
                 (if (<= z 470000000.0) (/ y z) x))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x / -z;
	double tmp;
	if (z <= -4e+89) {
		tmp = x;
	} else if (z <= -5.4e-41) {
		tmp = y / z;
	} else if (z <= -4.8e-83) {
		tmp = t_0;
	} else if (z <= -1.85e-102) {
		tmp = y / z;
	} else if (z <= -4.6e-245) {
		tmp = t_0;
	} else if (z <= 3.8e-198) {
		tmp = y / z;
	} else if (z <= 1.7e-19) {
		tmp = t_0;
	} else if (z <= 470000000.0) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x / -z
    if (z <= (-4d+89)) then
        tmp = x
    else if (z <= (-5.4d-41)) then
        tmp = y / z
    else if (z <= (-4.8d-83)) then
        tmp = t_0
    else if (z <= (-1.85d-102)) then
        tmp = y / z
    else if (z <= (-4.6d-245)) then
        tmp = t_0
    else if (z <= 3.8d-198) then
        tmp = y / z
    else if (z <= 1.7d-19) then
        tmp = t_0
    else if (z <= 470000000.0d0) 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 t_0 = x / -z;
	double tmp;
	if (z <= -4e+89) {
		tmp = x;
	} else if (z <= -5.4e-41) {
		tmp = y / z;
	} else if (z <= -4.8e-83) {
		tmp = t_0;
	} else if (z <= -1.85e-102) {
		tmp = y / z;
	} else if (z <= -4.6e-245) {
		tmp = t_0;
	} else if (z <= 3.8e-198) {
		tmp = y / z;
	} else if (z <= 1.7e-19) {
		tmp = t_0;
	} else if (z <= 470000000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x / -z
	tmp = 0
	if z <= -4e+89:
		tmp = x
	elif z <= -5.4e-41:
		tmp = y / z
	elif z <= -4.8e-83:
		tmp = t_0
	elif z <= -1.85e-102:
		tmp = y / z
	elif z <= -4.6e-245:
		tmp = t_0
	elif z <= 3.8e-198:
		tmp = y / z
	elif z <= 1.7e-19:
		tmp = t_0
	elif z <= 470000000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x / Float64(-z))
	tmp = 0.0
	if (z <= -4e+89)
		tmp = x;
	elseif (z <= -5.4e-41)
		tmp = Float64(y / z);
	elseif (z <= -4.8e-83)
		tmp = t_0;
	elseif (z <= -1.85e-102)
		tmp = Float64(y / z);
	elseif (z <= -4.6e-245)
		tmp = t_0;
	elseif (z <= 3.8e-198)
		tmp = Float64(y / z);
	elseif (z <= 1.7e-19)
		tmp = t_0;
	elseif (z <= 470000000.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x / -z;
	tmp = 0.0;
	if (z <= -4e+89)
		tmp = x;
	elseif (z <= -5.4e-41)
		tmp = y / z;
	elseif (z <= -4.8e-83)
		tmp = t_0;
	elseif (z <= -1.85e-102)
		tmp = y / z;
	elseif (z <= -4.6e-245)
		tmp = t_0;
	elseif (z <= 3.8e-198)
		tmp = y / z;
	elseif (z <= 1.7e-19)
		tmp = t_0;
	elseif (z <= 470000000.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x / (-z)), $MachinePrecision]}, If[LessEqual[z, -4e+89], x, If[LessEqual[z, -5.4e-41], N[(y / z), $MachinePrecision], If[LessEqual[z, -4.8e-83], t$95$0, If[LessEqual[z, -1.85e-102], N[(y / z), $MachinePrecision], If[LessEqual[z, -4.6e-245], t$95$0, If[LessEqual[z, 3.8e-198], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.7e-19], t$95$0, If[LessEqual[z, 470000000.0], N[(y / z), $MachinePrecision], x]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999998e89 or 4.7e8 < 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 77.4%

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

   if -3.99999999999999998e89 < z < -5.4e-41 or -4.8000000000000002e-83 < z < -1.8499999999999999e-102 or -4.6000000000000003e-245 < z < 3.8000000000000002e-198 or 1.7000000000000001e-19 < z < 4.7e8

   1. Initial program 100.0%

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

      1. div-sub 98.8%

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

      2. sub-neg 98.8%

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

      3. distribute-frac-neg 98.8%

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

      4. +-commutative 98.8%

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

      5. associate-+r+ 98.8%

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

      6. distribute-frac-neg 98.8%

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

      7. sub-neg 98.8%

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

      8. associate--r- 98.8%

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

      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 71.1%

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

   if -5.4e-41 < z < -4.8000000000000002e-83 or -1.8499999999999999e-102 < z < -4.6000000000000003e-245 or 3.8000000000000002e-198 < z < 1.7000000000000001e-19

   1. Initial program 99.9%

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

      1. div-sub 97.3%

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

      2. sub-neg 97.3%

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

      3. distribute-frac-neg 97.3%

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

      4. +-commutative 97.3%

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

      5. associate-+r+ 97.3%

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

      6. distribute-frac-neg 97.3%

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

      7. sub-neg 97.3%

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

      8. associate--r- 97.3%

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

      9. div-sub 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 66.8%

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

   6. Taylor expanded in z around 0 66.8%

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

      1. associate-*r/ 66.8%

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

      2. neg-mul-1 66.8%

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

   8. Simplified 66.8%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+89}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-83}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-198}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-19}:\\ \;\;\;\;\frac{x}{-z}\\ \mathbf{elif}\;z \leq 470000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -42 \lor \neg \left(z \leq 0.48\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -42.0) (not (<= z 0.48))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -42.0) || !(z <= 0.48)) {
		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 <= (-42.0d0)) .or. (.not. (z <= 0.48d0))) 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 <= -42.0) || !(z <= 0.48)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -42.0) or not (z <= 0.48):
		tmp = x + (y / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -42.0) || !(z <= 0.48))
		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 <= -42.0) || ~((z <= 0.48)))
		tmp = x + (y / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -42.0], N[Not[LessEqual[z, 0.48]], $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 < -42 or 0.47999999999999998 < 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 98.9%

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

      1. neg-mul-1 98.9%

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

      2. distribute-neg-frac2 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in x around 0 98.9%

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

      1. cancel-sign-sub-inv 98.9%

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

      2. metadata-eval 98.9%

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

      3. *-lft-identity 98.9%

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

      4. +-commutative 98.9%

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

   10. Simplified 98.9%

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

   if -42 < z < 0.47999999999999998

   1. Initial program 99.9%

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

      1. div-sub 97.7%

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

      2. sub-neg 97.7%

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

      3. distribute-frac-neg 97.7%

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

      4. +-commutative 97.7%

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

      5. associate-+r+ 97.7%

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

      6. distribute-frac-neg 97.7%

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

      7. sub-neg 97.7%

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

      8. associate--r- 97.7%

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

      9. div-sub 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 99.4%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -42 \lor \neg \left(z \leq 0.48\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+50} \lor \neg \left(x \leq 3.2 \cdot 10^{+34}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.55e+50) (not (<= x 3.2e+34))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.55e+50) || !(x <= 3.2e+34)) {
		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 <= (-1.55d+50)) .or. (.not. (x <= 3.2d+34))) 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 <= -1.55e+50) || !(x <= 3.2e+34)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.55e+50) or not (x <= 3.2e+34):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.55e+50) || !(x <= 3.2e+34))
		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 <= -1.55e+50) || ~((x <= 3.2e+34)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.55e+50], N[Not[LessEqual[x, 3.2e+34]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.55000000000000001e50 or 3.1999999999999998e34 < x

   1. Initial program 100.0%

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

      1. div-sub 97.3%

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

      2. sub-neg 97.3%

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

      3. distribute-frac-neg 97.3%

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

      4. +-commutative 97.3%

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

      5. associate-+r+ 97.3%

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

      6. distribute-frac-neg 97.3%

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

      7. sub-neg 97.3%

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

      8. associate--r- 97.3%

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

      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 inf 92.6%

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

   if -1.55000000000000001e50 < x < 3.1999999999999998e34

   1. Initial program 99.9%

      \[x + \frac{y - x}{z} \]
   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 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 84.9%

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

      1. neg-mul-1 84.9%

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

      2. distribute-neg-frac2 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in x around 0 84.9%

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

      1. cancel-sign-sub-inv 84.9%

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

      2. metadata-eval 84.9%

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

      3. *-lft-identity 84.9%

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

      4. +-commutative 84.9%

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

   10. Simplified 84.9%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+50} \lor \neg \left(x \leq 3.2 \cdot 10^{+34}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-112} \lor \neg \left(y \leq -2.5 \cdot 10^{-271}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.65e-112) (not (<= y -2.5e-271))) (+ x (/ y z)) (/ x (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e-112) || !(y <= -2.5e-271)) {
		tmp = x + (y / z);
	} else {
		tmp = x / -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.65d-112)) .or. (.not. (y <= (-2.5d-271)))) then
        tmp = x + (y / z)
    else
        tmp = x / -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.65e-112) || !(y <= -2.5e-271)) {
		tmp = x + (y / z);
	} else {
		tmp = x / -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.65e-112) or not (y <= -2.5e-271):
		tmp = x + (y / z)
	else:
		tmp = x / -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.65e-112) || !(y <= -2.5e-271))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(x / Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.65e-112) || ~((y <= -2.5e-271)))
		tmp = x + (y / z);
	else
		tmp = x / -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.65e-112], N[Not[LessEqual[y, -2.5e-271]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x / (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e-112 or -2.5000000000000001e-271 < y

   1. Initial program 100.0%

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

      1. div-sub 98.7%

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

      2. sub-neg 98.7%

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

      3. distribute-frac-neg 98.7%

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

      4. +-commutative 98.7%

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

      5. associate-+r+ 98.7%

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

      6. distribute-frac-neg 98.7%

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

      7. sub-neg 98.7%

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

      8. associate--r- 98.7%

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

      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 80.0%

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

      1. neg-mul-1 80.0%

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

      2. distribute-neg-frac2 80.0%

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

   7. Simplified 80.0%

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

   8. Taylor expanded in x around 0 80.0%

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

      1. cancel-sign-sub-inv 80.0%

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

      2. metadata-eval 80.0%

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

      3. *-lft-identity 80.0%

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

      4. +-commutative 80.0%

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

   10. Simplified 80.0%

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

   if -1.65e-112 < y < -2.5000000000000001e-271

   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 inf 92.6%

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

   6. Taylor expanded in z around 0 73.2%

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

      1. associate-*r/ 73.2%

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

      2. neg-mul-1 73.2%

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

   8. Simplified 73.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-112} \lor \neg \left(y \leq -2.5 \cdot 10^{-271}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+83}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 550000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.85e+83) x (if (<= z 550000000.0) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+83) {
		tmp = x;
	} else if (z <= 550000000.0) {
		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 <= (-1.85d+83)) then
        tmp = x
    else if (z <= 550000000.0d0) 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 <= -1.85e+83) {
		tmp = x;
	} else if (z <= 550000000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.85e+83:
		tmp = x
	elif z <= 550000000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.85e+83)
		tmp = x;
	elseif (z <= 550000000.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.85e+83)
		tmp = x;
	elseif (z <= 550000000.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.85e+83], x, If[LessEqual[z, 550000000.0], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8500000000000001e83 or 5.5e8 < 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 77.4%

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

   if -1.8500000000000001e83 < z < 5.5e8

   1. Initial program 99.9%

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

      1. div-sub 98.1%

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

      2. sub-neg 98.1%

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

      3. distribute-frac-neg 98.1%

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

      4. +-commutative 98.1%

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

      5. associate-+r+ 98.1%

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

      6. distribute-frac-neg 98.1%

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

      7. sub-neg 98.1%

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

      8. associate--r- 98.1%

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

      9. div-sub 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 55.4%

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

Alternative 7: 36.5% 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 98.8%

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

   2. sub-neg 98.8%

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

   3. distribute-frac-neg 98.8%

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

   4. +-commutative 98.8%

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

   5. associate-+r+ 98.8%

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

   6. distribute-frac-neg 98.8%

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

   7. sub-neg 98.8%

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

   8. associate--r- 98.8%

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

   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 33.9%

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))