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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 7

Speedup: 1.0×

• 20.1% 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 60.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-153}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-152}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-91}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10500000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.0)
     x
     (if (<= z -1.05e-153)
       t_0
       (if (<= z -6.8e-197)
         (/ y z)
         (if (<= z 6e-200)
           t_0
           (if (<= z 4.8e-152)
             (/ y z)
             (if (<= z 4.5e-91) t_0 (if (<= z 10500000000.0) (/ y z) x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.0) {
		tmp = x;
	} else if (z <= -1.05e-153) {
		tmp = t_0;
	} else if (z <= -6.8e-197) {
		tmp = y / z;
	} else if (z <= 6e-200) {
		tmp = t_0;
	} else if (z <= 4.8e-152) {
		tmp = y / z;
	} else if (z <= 4.5e-91) {
		tmp = t_0;
	} else if (z <= 10500000000.0) {
		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 <= (-1.0d0)) then
        tmp = x
    else if (z <= (-1.05d-153)) then
        tmp = t_0
    else if (z <= (-6.8d-197)) then
        tmp = y / z
    else if (z <= 6d-200) then
        tmp = t_0
    else if (z <= 4.8d-152) then
        tmp = y / z
    else if (z <= 4.5d-91) then
        tmp = t_0
    else if (z <= 10500000000.0d0) 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 <= -1.0) {
		tmp = x;
	} else if (z <= -1.05e-153) {
		tmp = t_0;
	} else if (z <= -6.8e-197) {
		tmp = y / z;
	} else if (z <= 6e-200) {
		tmp = t_0;
	} else if (z <= 4.8e-152) {
		tmp = y / z;
	} else if (z <= 4.5e-91) {
		tmp = t_0;
	} else if (z <= 10500000000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.0:
		tmp = x
	elif z <= -1.05e-153:
		tmp = t_0
	elif z <= -6.8e-197:
		tmp = y / z
	elif z <= 6e-200:
		tmp = t_0
	elif z <= 4.8e-152:
		tmp = y / z
	elif z <= 4.5e-91:
		tmp = t_0
	elif z <= 10500000000.0:
		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 <= -1.0)
		tmp = x;
	elseif (z <= -1.05e-153)
		tmp = t_0;
	elseif (z <= -6.8e-197)
		tmp = Float64(y / z);
	elseif (z <= 6e-200)
		tmp = t_0;
	elseif (z <= 4.8e-152)
		tmp = Float64(y / z);
	elseif (z <= 4.5e-91)
		tmp = t_0;
	elseif (z <= 10500000000.0)
		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 <= -1.0)
		tmp = x;
	elseif (z <= -1.05e-153)
		tmp = t_0;
	elseif (z <= -6.8e-197)
		tmp = y / z;
	elseif (z <= 6e-200)
		tmp = t_0;
	elseif (z <= 4.8e-152)
		tmp = y / z;
	elseif (z <= 4.5e-91)
		tmp = t_0;
	elseif (z <= 10500000000.0)
		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, -1.0], x, If[LessEqual[z, -1.05e-153], t$95$0, If[LessEqual[z, -6.8e-197], N[(y / z), $MachinePrecision], If[LessEqual[z, 6e-200], t$95$0, If[LessEqual[z, 4.8e-152], N[(y / z), $MachinePrecision], If[LessEqual[z, 4.5e-91], t$95$0, If[LessEqual[z, 10500000000.0], N[(y / z), $MachinePrecision], x]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1 or 1.05e10 < z

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 67.8%

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

   if -1 < z < -1.05000000000000002e-153 or -6.7999999999999996e-197 < z < 5.99999999999999989e-200 or 4.8e-152 < z < 4.49999999999999976e-91

   1. Initial program 100.0%

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

      1. div-sub 95.2%

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

      2. associate-+r- 95.2%

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

      3. remove-double-neg 95.2%

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

      4. distribute-frac-neg 95.2%

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

      5. unsub-neg 95.2%

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

      6. associate--r+ 95.2%

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

      7. +-commutative 95.2%

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

      8. distribute-frac-neg 95.2%

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

      9. sub-neg 95.2%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 71.9%

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

   6. Taylor expanded in z around 0 71.5%

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

      1. mul-1-neg 71.5%

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

      2. distribute-frac-neg 71.5%

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

   8. Simplified 71.5%

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

   if -1.05000000000000002e-153 < z < -6.7999999999999996e-197 or 5.99999999999999989e-200 < z < 4.8e-152 or 4.49999999999999976e-91 < z < 1.05e10

   1. Initial program 99.9%

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

      1. div-sub 96.0%

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

      2. associate-+r- 96.0%

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

      3. remove-double-neg 96.0%

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

      4. distribute-frac-neg 96.0%

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

      5. unsub-neg 96.0%

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

      6. associate--r+ 96.0%

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

      7. +-commutative 96.0%

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

      8. distribute-frac-neg 96.0%

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

      9. sub-neg 96.0%

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

      10. div-sub 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 71.3%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-153}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-197}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-200}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-152}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 10500000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{y}{z}\\ t_1 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{-43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-199}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (/ y z))) (t_1 (/ (- x) z)))
   (if (<= z -1.35e-43)
     t_0
     (if (<= z -7.2e-154)
       t_1
       (if (<= z -9.8e-199)
         (/ y z)
         (if (<= z 8.6e-198)
           t_1
           (if (<= z 1.35e-148) (/ y z) (if (<= z 9e-93) 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-43) {
		tmp = t_0;
	} else if (z <= -7.2e-154) {
		tmp = t_1;
	} else if (z <= -9.8e-199) {
		tmp = y / z;
	} else if (z <= 8.6e-198) {
		tmp = t_1;
	} else if (z <= 1.35e-148) {
		tmp = y / z;
	} else if (z <= 9e-93) {
		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-43)) then
        tmp = t_0
    else if (z <= (-7.2d-154)) then
        tmp = t_1
    else if (z <= (-9.8d-199)) then
        tmp = y / z
    else if (z <= 8.6d-198) then
        tmp = t_1
    else if (z <= 1.35d-148) then
        tmp = y / z
    else if (z <= 9d-93) 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-43) {
		tmp = t_0;
	} else if (z <= -7.2e-154) {
		tmp = t_1;
	} else if (z <= -9.8e-199) {
		tmp = y / z;
	} else if (z <= 8.6e-198) {
		tmp = t_1;
	} else if (z <= 1.35e-148) {
		tmp = y / z;
	} else if (z <= 9e-93) {
		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-43:
		tmp = t_0
	elif z <= -7.2e-154:
		tmp = t_1
	elif z <= -9.8e-199:
		tmp = y / z
	elif z <= 8.6e-198:
		tmp = t_1
	elif z <= 1.35e-148:
		tmp = y / z
	elif z <= 9e-93:
		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-43)
		tmp = t_0;
	elseif (z <= -7.2e-154)
		tmp = t_1;
	elseif (z <= -9.8e-199)
		tmp = Float64(y / z);
	elseif (z <= 8.6e-198)
		tmp = t_1;
	elseif (z <= 1.35e-148)
		tmp = Float64(y / z);
	elseif (z <= 9e-93)
		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-43)
		tmp = t_0;
	elseif (z <= -7.2e-154)
		tmp = t_1;
	elseif (z <= -9.8e-199)
		tmp = y / z;
	elseif (z <= 8.6e-198)
		tmp = t_1;
	elseif (z <= 1.35e-148)
		tmp = y / z;
	elseif (z <= 9e-93)
		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-43], t$95$0, If[LessEqual[z, -7.2e-154], t$95$1, If[LessEqual[z, -9.8e-199], N[(y / z), $MachinePrecision], If[LessEqual[z, 8.6e-198], t$95$1, If[LessEqual[z, 1.35e-148], N[(y / z), $MachinePrecision], If[LessEqual[z, 9e-93], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.34999999999999996e-43 or 9.0000000000000004e-93 < z

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 91.7%

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

      1. neg-mul-1 91.7%

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

      2. distribute-neg-frac 91.7%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in x around 0 91.7%

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

      1. +-commutative 91.7%

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

   10. Simplified 91.7%

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

   if -1.34999999999999996e-43 < z < -7.2000000000000006e-154 or -9.8e-199 < z < 8.6000000000000007e-198 or 1.34999999999999994e-148 < z < 9.0000000000000004e-93

   1. Initial program 100.0%

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

      1. div-sub 94.7%

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

      2. associate-+r- 94.7%

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

      3. remove-double-neg 94.7%

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

      4. distribute-frac-neg 94.7%

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

      5. unsub-neg 94.7%

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

      6. associate--r+ 94.7%

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

      7. +-commutative 94.7%

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

      8. distribute-frac-neg 94.7%

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

      9. sub-neg 94.7%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 75.2%

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

   6. Taylor expanded in z around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. distribute-frac-neg 75.2%

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

   8. Simplified 75.2%

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

   if -7.2000000000000006e-154 < z < -9.8e-199 or 8.6000000000000007e-198 < z < 1.34999999999999994e-148

   1. Initial program 100.0%

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

      1. div-sub 92.3%

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

      2. associate-+r- 92.3%

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

      3. remove-double-neg 92.3%

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

      4. distribute-frac-neg 92.3%

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

      5. unsub-neg 92.3%

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

      6. associate--r+ 92.3%

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

      7. +-commutative 92.3%

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

      8. distribute-frac-neg 92.3%

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

      9. sub-neg 92.3%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 77.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-43}:\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-154}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq -9.8 \cdot 10^{-199}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{-198}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-93}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -38000000000000 \lor \neg \left(x \leq 0.21\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -38000000000000.0) (not (<= x 0.21)))
   (- x (/ x z))
   (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -38000000000000.0) || !(x <= 0.21)) {
		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 <= (-38000000000000.0d0)) .or. (.not. (x <= 0.21d0))) 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 <= -38000000000000.0) || !(x <= 0.21)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -38000000000000.0) or not (x <= 0.21):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -38000000000000.0) || !(x <= 0.21))
		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 <= -38000000000000.0) || ~((x <= 0.21)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -38000000000000.0], N[Not[LessEqual[x, 0.21]], $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 < -3.8e13 or 0.209999999999999992 < x

   1. Initial program 100.0%

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

      1. div-sub 95.5%

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

      2. associate-+r- 95.5%

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

      3. remove-double-neg 95.5%

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

      4. distribute-frac-neg 95.5%

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

      5. unsub-neg 95.5%

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

      6. associate--r+ 95.5%

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

      7. +-commutative 95.5%

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

      8. distribute-frac-neg 95.5%

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

      9. sub-neg 95.5%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 88.5%

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

   if -3.8e13 < x < 0.209999999999999992

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 87.0%

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

      1. neg-mul-1 87.0%

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

      2. distribute-neg-frac 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around 0 87.0%

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

      1. +-commutative 87.0%

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

   10. Simplified 87.0%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -38000000000000 \lor \neg \left(x \leq 0.21\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.205\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.205))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.205)) {
		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 <= 0.205d0))) 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 <= 0.205)) {
		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 <= 0.205):
		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 <= 0.205))
		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 <= 0.205)))
		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, 0.205]], $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 0.204999999999999988 < z

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 99.1%

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

      1. neg-mul-1 99.1%

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

      2. distribute-neg-frac 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around 0 99.1%

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

      1. +-commutative 99.1%

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

   10. Simplified 99.1%

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

   if -1 < z < 0.204999999999999988

   1. Initial program 100.0%

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

      1. div-sub 95.4%

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

      2. associate-+r- 95.4%

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

      3. remove-double-neg 95.4%

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

      4. distribute-frac-neg 95.4%

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

      5. unsub-neg 95.4%

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

      6. associate--r+ 95.4%

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

      7. +-commutative 95.4%

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

      8. distribute-frac-neg 95.4%

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

      9. sub-neg 95.4%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 99.4%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.205\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 22000000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -8.6e+14) x (if (<= z 22000000000.0) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -8.6e+14) {
		tmp = x;
	} else if (z <= 22000000000.0) {
		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 <= (-8.6d+14)) then
        tmp = x
    else if (z <= 22000000000.0d0) 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 <= -8.6e+14) {
		tmp = x;
	} else if (z <= 22000000000.0) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -8.6e+14:
		tmp = x
	elif z <= 22000000000.0:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -8.6e+14)
		tmp = x;
	elseif (z <= 22000000000.0)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -8.6e+14)
		tmp = x;
	elseif (z <= 22000000000.0)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -8.6e+14], x, If[LessEqual[z, 22000000000.0], N[(y / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.6e14 or 2.2e10 < z

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. associate-+r- 100.0%

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

      3. remove-double-neg 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. associate--r+ 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-frac-neg 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 69.2%

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

   if -8.6e14 < z < 2.2e10

   1. Initial program 100.0%

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

      1. div-sub 95.6%

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

      2. associate-+r- 95.6%

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

      3. remove-double-neg 95.6%

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

      4. distribute-frac-neg 95.6%

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

      5. unsub-neg 95.6%

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

      6. associate--r+ 95.6%

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

      7. +-commutative 95.6%

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

      8. distribute-frac-neg 95.6%

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

      9. sub-neg 95.6%

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

      10. div-sub 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 48.5%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 22000000000:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.6% 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. Step-by-step derivation

   1. div-sub 97.7%

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

   2. associate-+r- 97.7%

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

   3. remove-double-neg 97.7%

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

   4. distribute-frac-neg 97.7%

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

   5. unsub-neg 97.7%

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

   6. associate--r+ 97.7%

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

   7. +-commutative 97.7%

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

   8. distribute-frac-neg 97.7%

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

   9. sub-neg 97.7%

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

   10. div-sub 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in z around inf 33.9%

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

6. Final simplification 33.9%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))