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

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 6

Speedup: 1.0×

• 20.8% 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: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{z} + x\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (/ y z) x)))
   (if (<= z -1.0) t_0 (if (<= z 1.05e-13) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y / z) + x;
	double tmp;
	if (z <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.05e-13) {
		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 <= (-1.0d0)) then
        tmp = t_0
    else if (z <= 1.05d-13) 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 <= -1.0) {
		tmp = t_0;
	} else if (z <= 1.05e-13) {
		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 <= -1.0:
		tmp = t_0
	elif z <= 1.05e-13:
		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 <= -1.0)
		tmp = t_0;
	elseif (z <= 1.05e-13)
		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 <= -1.0)
		tmp = t_0;
	elseif (z <= 1.05e-13)
		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, -1.0], t$95$0, If[LessEqual[z, 1.05e-13], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.04999999999999994e-13 < 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 98.8

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

   5. Applied rewrites 98.8%

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

   if -1 < z < 1.04999999999999994e-13

   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 99.5

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

   5. Applied rewrites 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{y}{z} + x\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-13}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{z}\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{+132}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+21}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x z))))
   (if (<= z -7.6e+132) t_0 (if (<= z 1.7e+21) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (z <= -7.6e+132) {
		tmp = t_0;
	} else if (z <= 1.7e+21) {
		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 <= (-7.6d+132)) then
        tmp = t_0
    else if (z <= 1.7d+21) 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 <= -7.6e+132) {
		tmp = t_0;
	} else if (z <= 1.7e+21) {
		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 <= -7.6e+132:
		tmp = t_0
	elif z <= 1.7e+21:
		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 <= -7.6e+132)
		tmp = t_0;
	elseif (z <= 1.7e+21)
		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 <= -7.6e+132)
		tmp = t_0;
	elseif (z <= 1.7e+21)
		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, -7.6e+132], t$95$0, If[LessEqual[z, 1.7e+21], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -7.60000000000000012e132 or 1.7e21 < z

   1. Initial program 99.9%

      \[x + \frac{y - x}{z} \]
   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 77.9

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

   5. Applied rewrites 77.9%

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

   if -7.60000000000000012e132 < z < 1.7e21

   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 92.4

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

   5. Applied rewrites 92.4%

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

Alternative 4: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{z}\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{-160}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x z))))
   (if (<= x -1.15e-160) t_0 (if (<= x 1.5e-111) (/ y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (x <= -1.15e-160) {
		tmp = t_0;
	} else if (x <= 1.5e-111) {
		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 <= (-1.15d-160)) then
        tmp = t_0
    else if (x <= 1.5d-111) 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 <= -1.15e-160) {
		tmp = t_0;
	} else if (x <= 1.5e-111) {
		tmp = y / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x - (x / z)
	tmp = 0
	if x <= -1.15e-160:
		tmp = t_0
	elif x <= 1.5e-111:
		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 <= -1.15e-160)
		tmp = t_0;
	elseif (x <= 1.5e-111)
		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 <= -1.15e-160)
		tmp = t_0;
	elseif (x <= 1.5e-111)
		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, -1.15e-160], t$95$0, If[LessEqual[x, 1.5e-111], N[(y / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14999999999999992e-160 or 1.50000000000000004e-111 < 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 80.6

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

   5. Applied rewrites 80.6%

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

   if -1.14999999999999992e-160 < x < 1.50000000000000004e-111

   1. Initial program 99.9%

      \[x + \frac{y - x}{z} \]
   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: 53.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= x -2.3e+33) t_0 (if (<= x 2.4e+31) (/ y z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (x <= -2.3e+33) {
		tmp = t_0;
	} else if (x <= 2.4e+31) {
		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 <= (-2.3d+33)) then
        tmp = t_0
    else if (x <= 2.4d+31) 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 <= -2.3e+33) {
		tmp = t_0;
	} else if (x <= 2.4e+31) {
		tmp = y / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if x <= -2.3e+33:
		tmp = t_0
	elif x <= 2.4e+31:
		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 <= -2.3e+33)
		tmp = t_0;
	elseif (x <= 2.4e+31)
		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 <= -2.3e+33)
		tmp = t_0;
	elseif (x <= 2.4e+31)
		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, -2.3e+33], t$95$0, If[LessEqual[x, 2.4e+31], N[(y / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.30000000000000011e33 or 2.39999999999999982e31 < 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 54.3

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

   5. Applied rewrites 54.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 43.8%

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

   if -2.30000000000000011e33 < x < 2.39999999999999982e31

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. lower-/.f64 57.0

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

   5. Applied rewrites 57.0%

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

Alternative 6: 42.6% 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 36.9

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

5. Applied rewrites 36.9%

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

Reproduce

herbie shell --seed 2024249 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))