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

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

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: 61.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -14:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-116}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-275}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -14.0)
     x
     (if (<= z -2.7e-116)
       (/ y z)
       (if (<= z -2.5e-197)
         t_0
         (if (<= z -1.1e-224)
           (/ y z)
           (if (<= z 4.3e-275)
             t_0
             (if (<= z 6.5e-196) (/ y z) (if (<= z 1.0) t_0 x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -14.0) {
		tmp = x;
	} else if (z <= -2.7e-116) {
		tmp = y / z;
	} else if (z <= -2.5e-197) {
		tmp = t_0;
	} else if (z <= -1.1e-224) {
		tmp = y / z;
	} else if (z <= 4.3e-275) {
		tmp = t_0;
	} else if (z <= 6.5e-196) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} 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 <= (-14.0d0)) then
        tmp = x
    else if (z <= (-2.7d-116)) then
        tmp = y / z
    else if (z <= (-2.5d-197)) then
        tmp = t_0
    else if (z <= (-1.1d-224)) then
        tmp = y / z
    else if (z <= 4.3d-275) then
        tmp = t_0
    else if (z <= 6.5d-196) then
        tmp = y / z
    else if (z <= 1.0d0) then
        tmp = t_0
    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 <= -14.0) {
		tmp = x;
	} else if (z <= -2.7e-116) {
		tmp = y / z;
	} else if (z <= -2.5e-197) {
		tmp = t_0;
	} else if (z <= -1.1e-224) {
		tmp = y / z;
	} else if (z <= 4.3e-275) {
		tmp = t_0;
	} else if (z <= 6.5e-196) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -14.0:
		tmp = x
	elif z <= -2.7e-116:
		tmp = y / z
	elif z <= -2.5e-197:
		tmp = t_0
	elif z <= -1.1e-224:
		tmp = y / z
	elif z <= 4.3e-275:
		tmp = t_0
	elif z <= 6.5e-196:
		tmp = y / z
	elif z <= 1.0:
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -14.0)
		tmp = x;
	elseif (z <= -2.7e-116)
		tmp = Float64(y / z);
	elseif (z <= -2.5e-197)
		tmp = t_0;
	elseif (z <= -1.1e-224)
		tmp = Float64(y / z);
	elseif (z <= 4.3e-275)
		tmp = t_0;
	elseif (z <= 6.5e-196)
		tmp = Float64(y / z);
	elseif (z <= 1.0)
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -14.0)
		tmp = x;
	elseif (z <= -2.7e-116)
		tmp = y / z;
	elseif (z <= -2.5e-197)
		tmp = t_0;
	elseif (z <= -1.1e-224)
		tmp = y / z;
	elseif (z <= 4.3e-275)
		tmp = t_0;
	elseif (z <= 6.5e-196)
		tmp = y / z;
	elseif (z <= 1.0)
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -14.0], x, If[LessEqual[z, -2.7e-116], N[(y / z), $MachinePrecision], If[LessEqual[z, -2.5e-197], t$95$0, If[LessEqual[z, -1.1e-224], N[(y / z), $MachinePrecision], If[LessEqual[z, 4.3e-275], t$95$0, If[LessEqual[z, 6.5e-196], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$0, x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -14 or 1 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 73.5%

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

   if -14 < z < -2.7e-116 or -2.5000000000000001e-197 < z < -1.1e-224 or 4.29999999999999976e-275 < z < 6.5000000000000004e-196

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 76.1%

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

   3. Taylor expanded in x around 0 75.6%

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

   if -2.7e-116 < z < -2.5000000000000001e-197 or -1.1e-224 < z < 4.29999999999999976e-275 or 6.5000000000000004e-196 < 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. div-sub 96.5%

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

      3. associate-+l- 96.5%

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

   3. Applied egg-rr 96.5%

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

   4. Taylor expanded in z around 0 96.5%

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

      1. sub-div 100.0%

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

      2. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 66.9%

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

      1. mul-1-neg 66.9%

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

      2. distribute-frac-neg 66.9%

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

   9. Simplified 66.9%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-116}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-197}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-224}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-275}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-116}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-227}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ (- x) z)))
   (if (<= z -1.35e-116)
     t_0
     (if (<= z -1.65e-196)
       t_1
       (if (<= z -1.55e-227)
         (/ y z)
         (if (<= z 2.3e-277)
           t_1
           (if (<= z 2.2e-196) (/ y z) (if (<= z 1.52e-86) 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 <= -1.35e-116) {
		tmp = t_0;
	} else if (z <= -1.65e-196) {
		tmp = t_1;
	} else if (z <= -1.55e-227) {
		tmp = y / z;
	} else if (z <= 2.3e-277) {
		tmp = t_1;
	} else if (z <= 2.2e-196) {
		tmp = y / z;
	} else if (z <= 1.52e-86) {
		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 <= (-1.35d-116)) then
        tmp = t_0
    else if (z <= (-1.65d-196)) then
        tmp = t_1
    else if (z <= (-1.55d-227)) then
        tmp = y / z
    else if (z <= 2.3d-277) then
        tmp = t_1
    else if (z <= 2.2d-196) then
        tmp = y / z
    else if (z <= 1.52d-86) 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 <= -1.35e-116) {
		tmp = t_0;
	} else if (z <= -1.65e-196) {
		tmp = t_1;
	} else if (z <= -1.55e-227) {
		tmp = y / z;
	} else if (z <= 2.3e-277) {
		tmp = t_1;
	} else if (z <= 2.2e-196) {
		tmp = y / z;
	} else if (z <= 1.52e-86) {
		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 <= -1.35e-116:
		tmp = t_0
	elif z <= -1.65e-196:
		tmp = t_1
	elif z <= -1.55e-227:
		tmp = y / z
	elif z <= 2.3e-277:
		tmp = t_1
	elif z <= 2.2e-196:
		tmp = y / z
	elif z <= 1.52e-86:
		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 <= -1.35e-116)
		tmp = t_0;
	elseif (z <= -1.65e-196)
		tmp = t_1;
	elseif (z <= -1.55e-227)
		tmp = Float64(y / z);
	elseif (z <= 2.3e-277)
		tmp = t_1;
	elseif (z <= 2.2e-196)
		tmp = Float64(y / z);
	elseif (z <= 1.52e-86)
		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 <= -1.35e-116)
		tmp = t_0;
	elseif (z <= -1.65e-196)
		tmp = t_1;
	elseif (z <= -1.55e-227)
		tmp = y / z;
	elseif (z <= 2.3e-277)
		tmp = t_1;
	elseif (z <= 2.2e-196)
		tmp = y / z;
	elseif (z <= 1.52e-86)
		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, -1.35e-116], t$95$0, If[LessEqual[z, -1.65e-196], t$95$1, If[LessEqual[z, -1.55e-227], N[(y / z), $MachinePrecision], If[LessEqual[z, 2.3e-277], t$95$1, If[LessEqual[z, 2.2e-196], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.52e-86], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.35e-116 or 1.52e-86 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 88.8%

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

   if -1.35e-116 < z < -1.64999999999999999e-196 or -1.5499999999999999e-227 < z < 2.3e-277 or 2.20000000000000015e-196 < z < 1.52e-86

   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. div-sub 95.5%

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

      3. associate-+l- 95.5%

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

   3. Applied egg-rr 95.5%

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

   4. Taylor expanded in z around 0 95.5%

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

      1. sub-div 100.0%

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

      2. clear-num 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. distribute-frac-neg 72.6%

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

   9. Simplified 72.6%

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

   if -1.64999999999999999e-196 < z < -1.5499999999999999e-227 or 2.3e-277 < z < 2.20000000000000015e-196

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 82.9%

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

   3. Taylor expanded in x around 0 83.0%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-196}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-227}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-277}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-196}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-86}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 4: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-7} \lor \neg \left(x \leq -1.9 \cdot 10^{-85} \lor \neg \left(x \leq -1.15 \cdot 10^{-157}\right) \land x \leq 90000000\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.3e-7)
         (not
          (or (<= x -1.9e-85)
              (and (not (<= x -1.15e-157)) (<= x 90000000.0)))))
   (- x (/ x z))
   (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.3e-7) || !((x <= -1.9e-85) || (!(x <= -1.15e-157) && (x <= 90000000.0)))) {
		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 <= (-4.3d-7)) .or. (.not. (x <= (-1.9d-85)) .or. (.not. (x <= (-1.15d-157))) .and. (x <= 90000000.0d0))) 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 <= -4.3e-7) || !((x <= -1.9e-85) || (!(x <= -1.15e-157) && (x <= 90000000.0)))) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.3e-7) or not ((x <= -1.9e-85) or (not (x <= -1.15e-157) and (x <= 90000000.0))):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.3e-7) || !((x <= -1.9e-85) || (!(x <= -1.15e-157) && (x <= 90000000.0))))
		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 <= -4.3e-7) || ~(((x <= -1.9e-85) || (~((x <= -1.15e-157)) && (x <= 90000000.0)))))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.3e-7], N[Not[Or[LessEqual[x, -1.9e-85], And[N[Not[LessEqual[x, -1.15e-157]], $MachinePrecision], LessEqual[x, 90000000.0]]]], $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 < -4.3000000000000001e-7 or -1.8999999999999999e-85 < x < -1.14999999999999994e-157 or 9e7 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 87.9%

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

   if -4.3000000000000001e-7 < x < -1.8999999999999999e-85 or -1.14999999999999994e-157 < x < 9e7

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.6%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.3 \cdot 10^{-7} \lor \neg \left(x \leq -1.9 \cdot 10^{-85} \lor \neg \left(x \leq -1.15 \cdot 10^{-157}\right) \land x \leq 90000000\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 5: 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 98.7%

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

   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. div-sub 96.3%

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

      3. associate-+l- 96.3%

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

   3. Applied egg-rr 96.3%

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

   4. Taylor expanded in z around 0 96.0%

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

      1. sub-div 99.7%

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

      2. clear-num 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in z around 0 99.7%

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

4. Final simplification 99.2%

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

Alternative 6: 61.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -14:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3500000000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -14.0) x (if (<= z 3500000000000.0) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -14.0) {
		tmp = x;
	} else if (z <= 3500000000000.0) {
		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 <= (-14.0d0)) then
        tmp = x
    else if (z <= 3500000000000.0d0) 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 <= -14.0) {
		tmp = x;
	} else if (z <= 3500000000000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -14.0:
		tmp = x
	elif z <= 3500000000000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -14.0)
		tmp = x;
	elseif (z <= 3500000000000.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -14.0)
		tmp = x;
	elseif (z <= 3500000000000.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -14.0], x, If[LessEqual[z, 3500000000000.0], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -14 or 3.5e12 < z

   1. Initial program 100.0%

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

   2. Taylor expanded in z around inf 74.0%

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

   if -14 < z < 3.5e12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 49.9%

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

   3. Taylor expanded in x around 0 49.7%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -14:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3500000000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 36.4% 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 35.9%

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

3. Final simplification 35.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))