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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 6

Speedup: 1.0×

• 20.7% 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((y - x) / z) + 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 = ((y - x) / z) + x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{z} + x\\ \mathbf{if}\;z \leq -66000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-24}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (/ y z) x)))
   (if (<= z -66000000000000.0) t_0 (if (<= z 1.25e-24) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y / z) + x;
	double tmp;
	if (z <= -66000000000000.0) {
		tmp = t_0;
	} else if (z <= 1.25e-24) {
		tmp = (y - x) / z;
	} 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 = (y / z) + x
    if (z <= (-66000000000000.0d0)) then
        tmp = t_0
    else if (z <= 1.25d-24) then
        tmp = (y - x) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y / z) + x;
	double tmp;
	if (z <= -66000000000000.0) {
		tmp = t_0;
	} else if (z <= 1.25e-24) {
		tmp = (y - x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y / z) + x
	tmp = 0
	if z <= -66000000000000.0:
		tmp = t_0
	elif z <= 1.25e-24:
		tmp = (y - x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y / z) + x)
	tmp = 0.0
	if (z <= -66000000000000.0)
		tmp = t_0;
	elseif (z <= 1.25e-24)
		tmp = Float64(Float64(y - x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y / z) + x;
	tmp = 0.0;
	if (z <= -66000000000000.0)
		tmp = t_0;
	elseif (z <= 1.25e-24)
		tmp = (y - x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y / z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[z, -66000000000000.0], t$95$0, If[LessEqual[z, 1.25e-24], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.6e13 or 1.24999999999999995e-24 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if -6.6e13 < z < 1.24999999999999995e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 99.4

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

   5. Applied rewrites 99.4%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -66000000000000:\\ \;\;\;\;\frac{y}{z} + x\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-24}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{z}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+32}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 235:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x z))))
   (if (<= z -1e+32) t_0 (if (<= z 235.0) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (z <= -1e+32) {
		tmp = t_0;
	} else if (z <= 235.0) {
		tmp = (y - x) / z;
	} 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 - (x / z)
    if (z <= (-1d+32)) then
        tmp = t_0
    else if (z <= 235.0d0) then
        tmp = (y - x) / z
    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 - (x / z);
	double tmp;
	if (z <= -1e+32) {
		tmp = t_0;
	} else if (z <= 235.0) {
		tmp = (y - x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (x / z)
	tmp = 0
	if z <= -1e+32:
		tmp = t_0
	elif z <= 235.0:
		tmp = (y - x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(x / z))
	tmp = 0.0
	if (z <= -1e+32)
		tmp = t_0;
	elseif (z <= 235.0)
		tmp = Float64(Float64(y - x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (x / z);
	tmp = 0.0;
	if (z <= -1e+32)
		tmp = t_0;
	elseif (z <= 235.0)
		tmp = (y - x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+32], t$95$0, If[LessEqual[z, 235.0], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.00000000000000005e32 or 235 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 70.8

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

   5. Applied rewrites 70.8%

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

   if -1.00000000000000005e32 < z < 235

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 98.6

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

   5. Applied rewrites 98.6%

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

Alternative 4: 74.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{z}\\ \mathbf{if}\;x \leq -12.6:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x z))))
   (if (<= x -12.6) t_0 (if (<= x 9.2e-42) (/ y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (x <= -12.6) {
		tmp = t_0;
	} else if (x <= 9.2e-42) {
		tmp = y / z;
	} 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 - (x / z)
    if (x <= (-12.6d0)) then
        tmp = t_0
    else if (x <= 9.2d-42) then
        tmp = y / z
    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 - (x / z);
	double tmp;
	if (x <= -12.6) {
		tmp = t_0;
	} else if (x <= 9.2e-42) {
		tmp = y / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (x / z)
	tmp = 0
	if x <= -12.6:
		tmp = t_0
	elif x <= 9.2e-42:
		tmp = y / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x - Float64(x / z))
	tmp = 0.0
	if (x <= -12.6)
		tmp = t_0;
	elseif (x <= 9.2e-42)
		tmp = Float64(y / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x - (x / z);
	tmp = 0.0;
	if (x <= -12.6)
		tmp = t_0;
	elseif (x <= 9.2e-42)
		tmp = y / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -12.6], t$95$0, If[LessEqual[x, 9.2e-42], N[(y / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -12.5999999999999996 or 9.20000000000000015e-42 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

      2. lower-/.f64 87.5

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

   5. Applied rewrites 87.5%

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

   if -12.5999999999999996 < x < 9.20000000000000015e-42

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 71.9

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

   5. Applied rewrites 71.9%

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

Alternative 5: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= x -8.5e+140) t_0 (if (<= x 1.22e-6) (/ y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (x <= -8.5e+140) {
		tmp = t_0;
	} else if (x <= 1.22e-6) {
		tmp = y / z;
	} 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 <= (-8.5d+140)) then
        tmp = t_0
    else if (x <= 1.22d-6) then
        tmp = y / z
    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 <= -8.5e+140) {
		tmp = t_0;
	} else if (x <= 1.22e-6) {
		tmp = y / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if x <= -8.5e+140:
		tmp = t_0
	elif x <= 1.22e-6:
		tmp = y / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (x <= -8.5e+140)
		tmp = t_0;
	elseif (x <= 1.22e-6)
		tmp = Float64(y / z);
	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 <= -8.5e+140)
		tmp = t_0;
	elseif (x <= 1.22e-6)
		tmp = y / z;
	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, -8.5e+140], t$95$0, If[LessEqual[x, 1.22e-6], N[(y / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.4999999999999996e140 or 1.21999999999999997e-6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 58.3

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

   5. Applied rewrites 58.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 48.4%

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

   if -8.4999999999999996e140 < x < 1.21999999999999997e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 62.2

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

   5. Applied rewrites 62.2%

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

Alternative 6: 42.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return y / 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 = y / z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf

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

   1. lower-/.f64 44.4

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

5. Applied rewrites 44.4%

   \[\leadsto \color{blue}{\frac{y}{z}} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024277 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))