Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3

Percentage Accurate: 84.4% → 96.1%

Time: 4.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

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 - z)) / y
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Python

def code(x, y, z):
	return (x * (y - z)) / y

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Initial Program: 84.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(y - z\right)}{y} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))

C

double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

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 - z)) / y
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}

Python

def code(x, y, z):
	return (x * (y - z)) / y

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y - z)) / y)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y - z)) / y;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]

Alternative 1: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \frac{z}{y}\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (/ z y))))

C

double code(double x, double y, double z) {
	return x * (1.0 - (z / y));
}

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 * (1.0d0 - (z / y))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - (z / y));
}

Python

def code(x, y, z):
	return x * (1.0 - (z / y))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(z / y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - (z / y));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.3%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*r/ 97.3%

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

   2. div-sub 97.3%

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

   3. *-inverses 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 68.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+100) x (if (<= y 5.2e+31) (* x (/ (- z) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+100) {
		tmp = x;
	} else if (y <= 5.2e+31) {
		tmp = x * (-z / y);
	} 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 (y <= (-6d+100)) then
        tmp = x
    else if (y <= 5.2d+31) then
        tmp = x * (-z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+100) {
		tmp = x;
	} else if (y <= 5.2e+31) {
		tmp = x * (-z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e+100:
		tmp = x
	elif y <= 5.2e+31:
		tmp = x * (-z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e+100)
		tmp = x;
	elseif (y <= 5.2e+31)
		tmp = Float64(x * Float64(Float64(-z) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e+100)
		tmp = x;
	elseif (y <= 5.2e+31)
		tmp = x * (-z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e+100], x, If[LessEqual[y, 5.2e+31], N[(x * N[((-z) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999971e100 or 5.2e31 < y

   1. Initial program 70.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 82.6%

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

   if -5.99999999999999971e100 < y < 5.2e31

   1. Initial program 93.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 95.6%

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

      2. div-sub 95.6%

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

      3. *-inverses 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in z around inf 70.0%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 70.0%

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

      2. distribute-frac-neg 70.0%

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

   6. Simplified 70.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+31}:\\ \;\;\;\;x \cdot \frac{-z}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.55e+100) x (if (<= y 3.8e+35) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+100) {
		tmp = x;
	} else if (y <= 3.8e+35) {
		tmp = z * (-x / y);
	} 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 (y <= (-1.55d+100)) then
        tmp = x
    else if (y <= 3.8d+35) then
        tmp = z * (-x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.55e+100) {
		tmp = x;
	} else if (y <= 3.8e+35) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.55e+100:
		tmp = x
	elif y <= 3.8e+35:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.55e+100)
		tmp = x;
	elseif (y <= 3.8e+35)
		tmp = Float64(z * Float64(Float64(-x) / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.55e+100)
		tmp = x;
	elseif (y <= 3.8e+35)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.55e+100], x, If[LessEqual[y, 3.8e+35], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000003e100 or 3.8e35 < y

   1. Initial program 70.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 82.6%

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

   if -1.55000000000000003e100 < y < 3.8e35

   1. Initial program 93.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 95.6%

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

      2. div-sub 95.6%

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

      3. *-inverses 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in z around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. *-commutative 72.0%

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

      3. associate-*r/ 70.6%

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

      4. distribute-rgt-neg-in 70.6%

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

   6. Simplified 70.6%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 71.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+100) x (if (<= y 6e+30) (/ z (/ (- y) x)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+100) {
		tmp = x;
	} else if (y <= 6e+30) {
		tmp = z / (-y / x);
	} 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 (y <= (-1.5d+100)) then
        tmp = x
    else if (y <= 6d+30) then
        tmp = z / (-y / x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+100) {
		tmp = x;
	} else if (y <= 6e+30) {
		tmp = z / (-y / x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+100:
		tmp = x
	elif y <= 6e+30:
		tmp = z / (-y / x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+100)
		tmp = x;
	elseif (y <= 6e+30)
		tmp = Float64(z / Float64(Float64(-y) / x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5e+100)
		tmp = x;
	elseif (y <= 6e+30)
		tmp = z / (-y / x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+100], x, If[LessEqual[y, 6e+30], N[(z / N[((-y) / x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.49999999999999993e100 or 5.99999999999999956e30 < y

   1. Initial program 70.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 82.6%

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

   if -1.49999999999999993e100 < y < 5.99999999999999956e30

   1. Initial program 93.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 95.6%

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

      2. div-sub 95.6%

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

      3. *-inverses 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in z around inf 70.0%

      \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{z}{y}\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 70.0%

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

      2. distribute-frac-neg 70.0%

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

   6. Simplified 70.0%

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

      1. *-commutative 70.0%

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

      2. associate-*l/ 72.0%

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

      3. distribute-lft-neg-in 72.0%

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

      4. distribute-rgt-neg-out 72.0%

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

      5. associate-/l* 71.2%

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

      6. frac-2neg 71.2%

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

      7. add-sqr-sqrt 35.4%

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

      8. sqrt-unprod 29.0%

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

      9. sqr-neg 29.0%

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

      10. sqrt-unprod 1.0%

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

      11. add-sqr-sqrt 2.0%

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

      12. add-sqr-sqrt 1.0%

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

      13. sqrt-unprod 29.8%

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

      14. sqr-neg 29.8%

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

      15. sqrt-unprod 35.5%

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

      16. add-sqr-sqrt 71.2%

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

      17. *-un-lft-identity 71.2%

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

      18. *-un-lft-identity 71.2%

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

   8. Applied egg-rr 71.2%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{\frac{-y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 70.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+31}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e+100) x (if (<= y 3.05e+31) (/ (* z (- x)) y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+100) {
		tmp = x;
	} else if (y <= 3.05e+31) {
		tmp = (z * -x) / y;
	} 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 (y <= (-2d+100)) then
        tmp = x
    else if (y <= 3.05d+31) then
        tmp = (z * -x) / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e+100) {
		tmp = x;
	} else if (y <= 3.05e+31) {
		tmp = (z * -x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e+100:
		tmp = x
	elif y <= 3.05e+31:
		tmp = (z * -x) / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e+100)
		tmp = x;
	elseif (y <= 3.05e+31)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2e+100)
		tmp = x;
	elseif (y <= 3.05e+31)
		tmp = (z * -x) / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e+100], x, If[LessEqual[y, 3.05e+31], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000003e100 or 3.05000000000000005e31 < y

   1. Initial program 70.0%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. div-sub 100.0%

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

      3. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around 0 82.6%

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

   if -2.00000000000000003e100 < y < 3.05000000000000005e31

   1. Initial program 93.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]

   2. Taylor expanded in y around 0 72.0%

      \[\leadsto \frac{\color{blue}{-1 \cdot \left(x \cdot z\right)}}{y} \]
   3. Step-by-step derivation

      1. associate-*r* 72.0%

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

      2. neg-mul-1 72.0%

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

      3. *-commutative 72.0%

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

   4. Simplified 72.0%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+100}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+31}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 51.6% 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 84.3%

   \[\frac{x \cdot \left(y - z\right)}{y} \]
2. Step-by-step derivation

   1. associate-*r/ 97.3%

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

   2. div-sub 97.3%

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

   3. *-inverses 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in z around 0 47.9%

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

5. Final simplification 47.9%

   \[\leadsto x \]

Developer target: 96.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z -2.060202331921739e+104)
   (- x (/ (* z x) y))
   (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	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 < (-2.060202331921739d+104)) then
        tmp = x - ((z * x) / y)
    else if (z < 1.6939766013828526d+213) then
        tmp = x / (y / (y - z))
    else
        tmp = (y - z) * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < -2.060202331921739e+104) {
		tmp = x - ((z * x) / y);
	} else if (z < 1.6939766013828526e+213) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (y - z) * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < -2.060202331921739e+104:
		tmp = x - ((z * x) / y)
	elif z < 1.6939766013828526e+213:
		tmp = x / (y / (y - z))
	else:
		tmp = (y - z) * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < -2.060202331921739e+104)
		tmp = Float64(x - Float64(Float64(z * x) / y));
	elseif (z < 1.6939766013828526e+213)
		tmp = Float64(x / Float64(y / Float64(y - z)));
	else
		tmp = Float64(Float64(y - z) * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < -2.060202331921739e+104)
		tmp = x - ((z * x) / y);
	elseif (z < 1.6939766013828526e+213)
		tmp = x / (y / (y - z));
	else
		tmp = (y - z) * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, -2.060202331921739e+104], N[(x - N[(N[(z * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Less[z, 1.6939766013828526e+213], N[(x / N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023309 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

  (/ (* x (- y z)) y))