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

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

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: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{z} + x\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.00027:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (/ y z) x)))
   (if (<= z -1.8e+19) t_0 (if (<= z 0.00027) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (y / z) + x;
	double tmp;
	if (z <= -1.8e+19) {
		tmp = t_0;
	} else if (z <= 0.00027) {
		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 <= (-1.8d+19)) then
        tmp = t_0
    else if (z <= 0.00027d0) 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 <= -1.8e+19) {
		tmp = t_0;
	} else if (z <= 0.00027) {
		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 <= -1.8e+19:
		tmp = t_0
	elif z <= 0.00027:
		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 <= -1.8e+19)
		tmp = t_0;
	elseif (z <= 0.00027)
		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 <= -1.8e+19)
		tmp = t_0;
	elseif (z <= 0.00027)
		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, -1.8e+19], t$95$0, If[LessEqual[z, 0.00027], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e19 or 2.70000000000000003e-4 < 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 99.6

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

   5. Applied rewrites 99.6%

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

   if -1.8e19 < z < 2.70000000000000003e-4

   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 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+19}:\\ \;\;\;\;\frac{y}{z} + x\\ \mathbf{elif}\;z \leq 0.00027:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+52}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+27}:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- x (/ x z))))
   (if (<= z -1.8e+52) t_0 (if (<= z 1.8e+27) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x - (x / z);
	double tmp;
	if (z <= -1.8e+52) {
		tmp = t_0;
	} else if (z <= 1.8e+27) {
		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 <= (-1.8d+52)) then
        tmp = t_0
    else if (z <= 1.8d+27) 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 <= -1.8e+52) {
		tmp = t_0;
	} else if (z <= 1.8e+27) {
		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 <= -1.8e+52:
		tmp = t_0
	elif z <= 1.8e+27:
		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 <= -1.8e+52)
		tmp = t_0;
	elseif (z <= 1.8e+27)
		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 <= -1.8e+52)
		tmp = t_0;
	elseif (z <= 1.8e+27)
		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, -1.8e+52], t$95$0, If[LessEqual[z, 1.8e+27], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e52 or 1.79999999999999991e27 < 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 78.9

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

   5. Applied rewrites 78.9%

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

   if -1.8e52 < z < 1.79999999999999991e27

   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 95.6

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

   5. Applied rewrites 95.6%

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

Alternative 4: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+117) (/ y z) (if (<= y 1.8e+55) (- x (/ x z)) (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+117) {
		tmp = y / z;
	} else if (y <= 1.8e+55) {
		tmp = x - (x / z);
	} else {
		tmp = 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 (y <= (-1.4d+117)) then
        tmp = y / z
    else if (y <= 1.8d+55) then
        tmp = x - (x / z)
    else
        tmp = y / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+117) {
		tmp = y / z;
	} else if (y <= 1.8e+55) {
		tmp = x - (x / z);
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e+117:
		tmp = y / z
	elif y <= 1.8e+55:
		tmp = x - (x / z)
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+117)
		tmp = Float64(y / z);
	elseif (y <= 1.8e+55)
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(y / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e+117)
		tmp = y / z;
	elseif (y <= 1.8e+55)
		tmp = x - (x / z);
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e+117], N[(y / z), $MachinePrecision], If[LessEqual[y, 1.8e+55], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999999e117 or 1.79999999999999994e55 < y

   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 75.7

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

   5. Applied rewrites 75.7%

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

   if -1.39999999999999999e117 < y < 1.79999999999999994e55

   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 82.4

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

   5. Applied rewrites 82.4%

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

Alternative 5: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-119}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.15e-39) (/ y z) (if (<= y 3.6e-119) (/ (- x) z) (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e-39) {
		tmp = y / z;
	} else if (y <= 3.6e-119) {
		tmp = -x / z;
	} else {
		tmp = 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 (y <= (-2.15d-39)) then
        tmp = y / z
    else if (y <= 3.6d-119) then
        tmp = -x / z
    else
        tmp = y / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e-39) {
		tmp = y / z;
	} else if (y <= 3.6e-119) {
		tmp = -x / z;
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2.15e-39:
		tmp = y / z
	elif y <= 3.6e-119:
		tmp = -x / z
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.15e-39)
		tmp = Float64(y / z);
	elseif (y <= 3.6e-119)
		tmp = Float64(Float64(-x) / z);
	else
		tmp = Float64(y / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.15e-39)
		tmp = y / z;
	elseif (y <= 3.6e-119)
		tmp = -x / z;
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.15e-39], N[(y / z), $MachinePrecision], If[LessEqual[y, 3.6e-119], N[((-x) / z), $MachinePrecision], N[(y / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15e-39 or 3.6e-119 < y

   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 61.1

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

   5. Applied rewrites 61.1%

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

   if -2.15e-39 < y < 3.6e-119

   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 46.5

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

   5. Applied rewrites 46.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 42.5%

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

Alternative 6: 42.0% 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 39.5

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

5. Applied rewrites 39.5%

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

Reproduce

herbie shell --seed 2024243 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))