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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 7

Speedup: 1.0×

• 20.9% 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. Final simplification 100.0%

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

Alternative 2: 60.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-119}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-222}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-223}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 36000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.4e+118)
     x
     (if (<= z -3.8e+86)
       (/ y z)
       (if (<= z -1.0)
         x
         (if (<= z -2.45e-119)
           t_0
           (if (<= z -9.8e-222)
             (/ y z)
             (if (<= z 3.1e-223)
               t_0
               (if (<= z 3.6e-86)
                 (/ y z)
                 (if (<= z 2.2e-39)
                   t_0
                   (if (<= z 36000000.0) (/ y z) x)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.4e+118) {
		tmp = x;
	} else if (z <= -3.8e+86) {
		tmp = y / z;
	} else if (z <= -1.0) {
		tmp = x;
	} else if (z <= -2.45e-119) {
		tmp = t_0;
	} else if (z <= -9.8e-222) {
		tmp = y / z;
	} else if (z <= 3.1e-223) {
		tmp = t_0;
	} else if (z <= 3.6e-86) {
		tmp = y / z;
	} else if (z <= 2.2e-39) {
		tmp = t_0;
	} else if (z <= 36000000.0) {
		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 <= (-1.4d+118)) then
        tmp = x
    else if (z <= (-3.8d+86)) then
        tmp = y / z
    else if (z <= (-1.0d0)) then
        tmp = x
    else if (z <= (-2.45d-119)) then
        tmp = t_0
    else if (z <= (-9.8d-222)) then
        tmp = y / z
    else if (z <= 3.1d-223) then
        tmp = t_0
    else if (z <= 3.6d-86) then
        tmp = y / z
    else if (z <= 2.2d-39) then
        tmp = t_0
    else if (z <= 36000000.0d0) 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 <= -1.4e+118) {
		tmp = x;
	} else if (z <= -3.8e+86) {
		tmp = y / z;
	} else if (z <= -1.0) {
		tmp = x;
	} else if (z <= -2.45e-119) {
		tmp = t_0;
	} else if (z <= -9.8e-222) {
		tmp = y / z;
	} else if (z <= 3.1e-223) {
		tmp = t_0;
	} else if (z <= 3.6e-86) {
		tmp = y / z;
	} else if (z <= 2.2e-39) {
		tmp = t_0;
	} else if (z <= 36000000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.4e+118:
		tmp = x
	elif z <= -3.8e+86:
		tmp = y / z
	elif z <= -1.0:
		tmp = x
	elif z <= -2.45e-119:
		tmp = t_0
	elif z <= -9.8e-222:
		tmp = y / z
	elif z <= 3.1e-223:
		tmp = t_0
	elif z <= 3.6e-86:
		tmp = y / z
	elif z <= 2.2e-39:
		tmp = t_0
	elif z <= 36000000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -1.4e+118)
		tmp = x;
	elseif (z <= -3.8e+86)
		tmp = Float64(y / z);
	elseif (z <= -1.0)
		tmp = x;
	elseif (z <= -2.45e-119)
		tmp = t_0;
	elseif (z <= -9.8e-222)
		tmp = Float64(y / z);
	elseif (z <= 3.1e-223)
		tmp = t_0;
	elseif (z <= 3.6e-86)
		tmp = Float64(y / z);
	elseif (z <= 2.2e-39)
		tmp = t_0;
	elseif (z <= 36000000.0)
		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 <= -1.4e+118)
		tmp = x;
	elseif (z <= -3.8e+86)
		tmp = y / z;
	elseif (z <= -1.0)
		tmp = x;
	elseif (z <= -2.45e-119)
		tmp = t_0;
	elseif (z <= -9.8e-222)
		tmp = y / z;
	elseif (z <= 3.1e-223)
		tmp = t_0;
	elseif (z <= 3.6e-86)
		tmp = y / z;
	elseif (z <= 2.2e-39)
		tmp = t_0;
	elseif (z <= 36000000.0)
		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, -1.4e+118], x, If[LessEqual[z, -3.8e+86], N[(y / z), $MachinePrecision], If[LessEqual[z, -1.0], x, If[LessEqual[z, -2.45e-119], t$95$0, If[LessEqual[z, -9.8e-222], N[(y / z), $MachinePrecision], If[LessEqual[z, 3.1e-223], t$95$0, If[LessEqual[z, 3.6e-86], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.2e-39], t$95$0, If[LessEqual[z, 36000000.0], N[(y / z), $MachinePrecision], x]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.39999999999999993e118 or -3.79999999999999978e86 < z < -1 or 3.6e7 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.1%

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

   if -1.39999999999999993e118 < z < -3.79999999999999978e86 or -2.45e-119 < z < -9.7999999999999999e-222 or 3.10000000000000018e-223 < z < 3.59999999999999966e-86 or 2.20000000000000001e-39 < z < 3.6e7

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. clear-num 99.8%

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

      3. associate-/r/ 99.9%

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

      4. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 71.5%

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

   if -1 < z < -2.45e-119 or -9.7999999999999999e-222 < z < 3.10000000000000018e-223 or 3.59999999999999966e-86 < z < 2.20000000000000001e-39

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.0%

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

   3. Taylor expanded in z around 0 70.2%

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

      1. neg-mul-1 70.2%

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

      2. distribute-frac-neg 70.2%

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

   5. Simplified 70.2%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+86}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-119}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-222}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-223}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-86}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 36000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 75.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-220}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-222}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-36}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ (- x) z)))
   (if (<= z -4.6e-10)
     t_0
     (if (<= z -6e-101)
       t_1
       (if (<= z -5.5e-220)
         t_0
         (if (<= z 1.9e-222)
           t_1
           (if (<= z 2.45e-85) (/ y z) (if (<= z 4e-36) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y / z);
	double t_1 = -x / z;
	double tmp;
	if (z <= -4.6e-10) {
		tmp = t_0;
	} else if (z <= -6e-101) {
		tmp = t_1;
	} else if (z <= -5.5e-220) {
		tmp = t_0;
	} else if (z <= 1.9e-222) {
		tmp = t_1;
	} else if (z <= 2.45e-85) {
		tmp = y / z;
	} else if (z <= 4e-36) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x + (y / z)
    t_1 = -x / z
    if (z <= (-4.6d-10)) then
        tmp = t_0
    else if (z <= (-6d-101)) then
        tmp = t_1
    else if (z <= (-5.5d-220)) then
        tmp = t_0
    else if (z <= 1.9d-222) then
        tmp = t_1
    else if (z <= 2.45d-85) then
        tmp = y / z
    else if (z <= 4d-36) then
        tmp = t_1
    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 + (y / z);
	double t_1 = -x / z;
	double tmp;
	if (z <= -4.6e-10) {
		tmp = t_0;
	} else if (z <= -6e-101) {
		tmp = t_1;
	} else if (z <= -5.5e-220) {
		tmp = t_0;
	} else if (z <= 1.9e-222) {
		tmp = t_1;
	} else if (z <= 2.45e-85) {
		tmp = y / z;
	} else if (z <= 4e-36) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y / z)
	t_1 = -x / z
	tmp = 0
	if z <= -4.6e-10:
		tmp = t_0
	elif z <= -6e-101:
		tmp = t_1
	elif z <= -5.5e-220:
		tmp = t_0
	elif z <= 1.9e-222:
		tmp = t_1
	elif z <= 2.45e-85:
		tmp = y / z
	elif z <= 4e-36:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y / z))
	t_1 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -4.6e-10)
		tmp = t_0;
	elseif (z <= -6e-101)
		tmp = t_1;
	elseif (z <= -5.5e-220)
		tmp = t_0;
	elseif (z <= 1.9e-222)
		tmp = t_1;
	elseif (z <= 2.45e-85)
		tmp = Float64(y / z);
	elseif (z <= 4e-36)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y / z);
	t_1 = -x / z;
	tmp = 0.0;
	if (z <= -4.6e-10)
		tmp = t_0;
	elseif (z <= -6e-101)
		tmp = t_1;
	elseif (z <= -5.5e-220)
		tmp = t_0;
	elseif (z <= 1.9e-222)
		tmp = t_1;
	elseif (z <= 2.45e-85)
		tmp = y / z;
	elseif (z <= 4e-36)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -4.6e-10], t$95$0, If[LessEqual[z, -6e-101], t$95$1, If[LessEqual[z, -5.5e-220], t$95$0, If[LessEqual[z, 1.9e-222], t$95$1, If[LessEqual[z, 2.45e-85], N[(y / z), $MachinePrecision], If[LessEqual[z, 4e-36], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.60000000000000014e-10 or -6.0000000000000006e-101 < z < -5.4999999999999999e-220 or 3.9999999999999998e-36 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 92.6%

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

   if -4.60000000000000014e-10 < z < -6.0000000000000006e-101 or -5.4999999999999999e-220 < z < 1.89999999999999998e-222 or 2.45000000000000007e-85 < z < 3.9999999999999998e-36

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 72.7%

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

   3. Taylor expanded in z around 0 71.8%

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

      1. neg-mul-1 71.8%

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

      2. distribute-frac-neg 71.8%

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

   5. Simplified 71.8%

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

   if 1.89999999999999998e-222 < z < 2.45000000000000007e-85

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. clear-num 99.9%

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

      3. associate-/r/ 99.9%

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

      4. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 63.5%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-101}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-220}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-222}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-85}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-36}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 4: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -190000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 65000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e+118)
   x
   (if (<= z -1.6e+87)
     (/ y z)
     (if (<= z -190000000000.0) x (if (<= z 65000000.0) (/ y z) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e+118) {
		tmp = x;
	} else if (z <= -1.6e+87) {
		tmp = y / z;
	} else if (z <= -190000000000.0) {
		tmp = x;
	} else if (z <= 65000000.0) {
		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 <= (-1.2d+118)) then
        tmp = x
    else if (z <= (-1.6d+87)) then
        tmp = y / z
    else if (z <= (-190000000000.0d0)) then
        tmp = x
    else if (z <= 65000000.0d0) 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 <= -1.2e+118) {
		tmp = x;
	} else if (z <= -1.6e+87) {
		tmp = y / z;
	} else if (z <= -190000000000.0) {
		tmp = x;
	} else if (z <= 65000000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e+118:
		tmp = x
	elif z <= -1.6e+87:
		tmp = y / z
	elif z <= -190000000000.0:
		tmp = x
	elif z <= 65000000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e+118)
		tmp = x;
	elseif (z <= -1.6e+87)
		tmp = Float64(y / z);
	elseif (z <= -190000000000.0)
		tmp = x;
	elseif (z <= 65000000.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.2e+118)
		tmp = x;
	elseif (z <= -1.6e+87)
		tmp = y / z;
	elseif (z <= -190000000000.0)
		tmp = x;
	elseif (z <= 65000000.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e+118], x, If[LessEqual[z, -1.6e+87], N[(y / z), $MachinePrecision], If[LessEqual[z, -190000000000.0], x, If[LessEqual[z, 65000000.0], N[(y / z), $MachinePrecision], x]]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e118 or -1.6e87 < z < -1.9e11 or 6.5e7 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 74.1%

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

   if -1.2e118 < z < -1.6e87 or -1.9e11 < z < 6.5e7

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. clear-num 99.7%

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

      3. associate-/r/ 99.8%

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

      4. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   4. Taylor expanded in y around inf 50.7%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{+87}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -190000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 65000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -65000000000000 \lor \neg \left(x \leq 7 \cdot 10^{-38}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -65000000000000.0) (not (<= x 7e-38)))
   (- x (/ x z))
   (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -65000000000000.0) || !(x <= 7e-38)) {
		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 <= (-65000000000000.0d0)) .or. (.not. (x <= 7d-38))) 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 <= -65000000000000.0) || !(x <= 7e-38)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -65000000000000.0) or not (x <= 7e-38):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -65000000000000.0) || !(x <= 7e-38))
		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 <= -65000000000000.0) || ~((x <= 7e-38)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -65000000000000.0], N[Not[LessEqual[x, 7e-38]], $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 < -6.5e13 or 7.0000000000000003e-38 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 88.7%

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

   if -6.5e13 < x < 7.0000000000000003e-38

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.7%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -65000000000000 \lor \neg \left(x \leq 7 \cdot 10^{-38}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 6: 98.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		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 <= 1.0d0))) 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 <= 1.0)) {
		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 <= 1.0):
		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 <= 1.0))
		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 <= 1.0)))
		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, 1.0]], $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 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.5%

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

   if -1 < z < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. clear-num 99.7%

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

      3. associate-/r/ 99.8%

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

      4. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   3. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{1}{z}, y - x, x\right)} \]

   4. Taylor expanded in z around 0 99.5%

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

4. Final simplification 99.0%

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

Alternative 7: 37.5% 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. Taylor expanded in z around inf 36.2%

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

3. Final simplification 36.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))