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

Percentage Accurate: 84.5% → 96.2%

Time: 6.5s

Alternatives: 7

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: 84.5% 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: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{y}{y - z}} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x / (y / (y - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.9%

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

   1. add-cube-cbrt 84.5%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x \cdot \left(y - z\right)}{y}} \cdot \sqrt[3]{\frac{x \cdot \left(y - z\right)}{y}}\right) \cdot \sqrt[3]{\frac{x \cdot \left(y - z\right)}{y}}} \]

   2. pow3 84.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{x \cdot \left(y - z\right)}{y}}\right)}^{3}} \]

   3. associate-/l* 95.2%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x \cdot \frac{y - z}{y}}}\right)}^{3} \]

4. Applied egg-rr 95.2%

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

   1. rem-cube-cbrt 96.9%

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

   2. clear-num 96.8%

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

   3. un-div-inv 97.1%

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

6. Applied egg-rr 97.1%

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

Alternative 2: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-46} \lor \neg \left(z \leq 9.6 \cdot 10^{-17}\right):\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.5e-46) (not (<= z 9.6e-17))) (* z (/ x (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.5e-46) || !(z <= 9.6e-17)) {
		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 ((z <= (-3.5d-46)) .or. (.not. (z <= 9.6d-17))) 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 ((z <= -3.5e-46) || !(z <= 9.6e-17)) {
		tmp = z * (x / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.5e-46) or not (z <= 9.6e-17):
		tmp = z * (x / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.5e-46) || !(z <= 9.6e-17))
		tmp = Float64(z * Float64(x / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.5e-46) || ~((z <= 9.6e-17)))
		tmp = z * (x / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.5e-46], N[Not[LessEqual[z, 9.6e-17]], $MachinePrecision]], N[(z * N[(x / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.5000000000000002e-46 or 9.59999999999999945e-17 < z

   1. Initial program 88.1%

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

      1. remove-double-neg 88.1%

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

      2. distribute-frac-neg2 88.1%

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

      3. distribute-frac-neg 88.1%

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

      4. distribute-rgt-neg-in 88.1%

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

      5. associate-/l* 94.1%

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

      6. distribute-frac-neg 94.1%

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

      7. distribute-frac-neg2 94.1%

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

      8. remove-double-neg 94.1%

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

      9. div-sub 94.1%

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

      10. *-inverses 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in z around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. distribute-frac-neg2 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-/l* 74.5%

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

   7. Simplified 74.5%

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

   if -3.5000000000000002e-46 < z < 9.59999999999999945e-17

   1. Initial program 83.6%

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

      1. remove-double-neg 83.6%

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

      2. distribute-frac-neg2 83.6%

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

      3. distribute-frac-neg 83.6%

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

      4. distribute-rgt-neg-in 83.6%

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

      5. associate-/l* 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. remove-double-neg 99.9%

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

      9. div-sub 99.9%

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

      10. *-inverses 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around 0 78.1%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-46} \lor \neg \left(z \leq 9.6 \cdot 10^{-17}\right):\\ \;\;\;\;z \cdot \frac{x}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-46} \lor \neg \left(z \leq 6.5 \cdot 10^{-118}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.8e-46) (not (<= z 6.5e-118))) (* x (/ z (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.8e-46) || !(z <= 6.5e-118)) {
		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 ((z <= (-3.8d-46)) .or. (.not. (z <= 6.5d-118))) 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 ((z <= -3.8e-46) || !(z <= 6.5e-118)) {
		tmp = x * (z / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.8e-46) or not (z <= 6.5e-118):
		tmp = x * (z / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.8e-46) || !(z <= 6.5e-118))
		tmp = Float64(x * Float64(z / Float64(-y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.8e-46) || ~((z <= 6.5e-118)))
		tmp = x * (z / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.8e-46], N[Not[LessEqual[z, 6.5e-118]], $MachinePrecision]], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.7999999999999997e-46 or 6.49999999999999958e-118 < z

   1. Initial program 88.6%

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

      1. remove-double-neg 88.6%

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

      2. distribute-frac-neg2 88.6%

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

      3. distribute-frac-neg 88.6%

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

      4. distribute-rgt-neg-in 88.6%

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

      5. associate-/l* 94.8%

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

      6. distribute-frac-neg 94.8%

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

      7. distribute-frac-neg2 94.8%

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

      8. remove-double-neg 94.8%

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

      9. div-sub 94.8%

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

      10. *-inverses 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 70.2%

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

      1. mul-1-neg 70.2%

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

      2. distribute-frac-neg2 70.2%

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

      3. associate-*r/ 67.6%

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

   7. Simplified 67.6%

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

   if -3.7999999999999997e-46 < z < 6.49999999999999958e-118

   1. Initial program 82.0%

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

      1. remove-double-neg 82.0%

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

      2. distribute-frac-neg2 82.0%

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

      3. distribute-frac-neg 82.0%

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

      4. distribute-rgt-neg-in 82.0%

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

      5. associate-/l* 100.0%

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

      6. distribute-frac-neg 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. remove-double-neg 100.0%

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

      9. div-sub 100.0%

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

      10. *-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. Add Preprocessing

   5. Taylor expanded in z around 0 83.3%

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

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-46} \lor \neg \left(z \leq 6.5 \cdot 10^{-118}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{+241}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 2.5e+241) x (/ y (/ y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.5e+241) {
		tmp = x;
	} else {
		tmp = y / (y / 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 (x <= 2.5d+241) then
        tmp = x
    else
        tmp = y / (y / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.5e+241) {
		tmp = x;
	} else {
		tmp = y / (y / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.5e+241:
		tmp = x
	else:
		tmp = y / (y / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.5e+241)
		tmp = x;
	else
		tmp = Float64(y / Float64(y / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.5e+241)
		tmp = x;
	else
		tmp = y / (y / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.5e+241], x, N[(y / N[(y / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.50000000000000013e241

   1. Initial program 87.9%

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

      1. remove-double-neg 87.9%

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

      2. distribute-frac-neg2 87.9%

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

      3. distribute-frac-neg 87.9%

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

      4. distribute-rgt-neg-in 87.9%

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

      5. associate-/l* 96.7%

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

      6. distribute-frac-neg 96.7%

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

      7. distribute-frac-neg2 96.7%

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

      8. remove-double-neg 96.7%

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

      9. div-sub 96.7%

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

      10. *-inverses 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 51.8%

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

   if 2.50000000000000013e241 < x

   1. Initial program 61.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 25.9%

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

      1. *-commutative 25.9%

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

      2. associate-/l* 65.2%

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

   5. Applied egg-rr 65.2%

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

      1. clear-num 65.2%

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

      2. un-div-inv 65.3%

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

   7. Applied egg-rr 65.3%

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

Alternative 5: 51.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.9 \cdot 10^{+242}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 6.9e+242) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.9e+242) {
		tmp = x;
	} else {
		tmp = y * (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 (x <= 6.9d+242) then
        tmp = x
    else
        tmp = y * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= 6.9e+242) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 6.9e+242:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 6.9e+242)
		tmp = x;
	else
		tmp = Float64(y * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 6.9e+242)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 6.9e+242], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.90000000000000017e242

   1. Initial program 87.9%

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

      1. remove-double-neg 87.9%

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

      2. distribute-frac-neg2 87.9%

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

      3. distribute-frac-neg 87.9%

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

      4. distribute-rgt-neg-in 87.9%

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

      5. associate-/l* 96.7%

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

      6. distribute-frac-neg 96.7%

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

      7. distribute-frac-neg2 96.7%

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

      8. remove-double-neg 96.7%

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

      9. div-sub 96.7%

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

      10. *-inverses 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 51.8%

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

   if 6.90000000000000017e242 < x

   1. Initial program 61.2%

      \[\frac{x \cdot \left(y - z\right)}{y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 25.9%

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

      1. *-commutative 25.9%

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

      2. associate-/l* 65.2%

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

   5. Applied egg-rr 65.2%

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

Alternative 6: 96.0% 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 85.9%

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

   1. remove-double-neg 85.9%

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

   2. distribute-frac-neg2 85.9%

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

   3. distribute-frac-neg 85.9%

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

   4. distribute-rgt-neg-in 85.9%

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

   5. associate-/l* 96.9%

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

   6. distribute-frac-neg 96.9%

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

   7. distribute-frac-neg2 96.9%

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

   8. remove-double-neg 96.9%

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

   9. div-sub 96.9%

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

   10. *-inverses 96.9%

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

3. Simplified 96.9%

   \[\leadsto \color{blue}{x \cdot \left(1 - \frac{z}{y}\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 7: 51.3% 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 85.9%

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

   1. remove-double-neg 85.9%

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

   2. distribute-frac-neg2 85.9%

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

   3. distribute-frac-neg 85.9%

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

   4. distribute-rgt-neg-in 85.9%

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

   5. associate-/l* 96.9%

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

   6. distribute-frac-neg 96.9%

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

   7. distribute-frac-neg2 96.9%

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

   8. remove-double-neg 96.9%

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

   9. div-sub 96.9%

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

   10. *-inverses 96.9%

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

3. Simplified 96.9%

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

5. Taylor expanded in z around 0 52.1%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.2% accurate, 0.4× 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 2024170 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -206020233192173900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* z x) y)) (if (< z 1693976601382852600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ x (/ y (- y z))) (* (- y z) (/ x y)))))

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