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

Percentage Accurate: 84.4% → 96.0%

Time: 7.3s

Alternatives: 5

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: 96.0% 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 83.2%

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

   1. remove-double-neg 83.2%

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

   2. distribute-frac-neg2 83.2%

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

   3. distribute-frac-neg 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. associate-/l* 97.6%

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

   6. distribute-frac-neg 97.6%

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

   7. distribute-frac-neg2 97.6%

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

   8. remove-double-neg 97.6%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

Alternative 2: 69.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -205 \lor \neg \left(z \leq 1.4 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -205.0) (not (<= z 1.4e-77))) (* x (/ z (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -205.0) || !(z <= 1.4e-77)) {
		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 <= (-205.0d0)) .or. (.not. (z <= 1.4d-77))) 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 <= -205.0) || !(z <= 1.4e-77)) {
		tmp = x * (z / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -205.0) or not (z <= 1.4e-77):
		tmp = x * (z / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -205.0) || !(z <= 1.4e-77))
		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 <= -205.0) || ~((z <= 1.4e-77)))
		tmp = x * (z / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -205.0], N[Not[LessEqual[z, 1.4e-77]], $MachinePrecision]], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -205 or 1.4e-77 < z

   1. Initial program 87.3%

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

      1. remove-double-neg 87.3%

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

      2. distribute-frac-neg2 87.3%

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

      3. distribute-frac-neg 87.3%

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

      4. distribute-rgt-neg-in 87.3%

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

      5. associate-/l* 95.9%

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

      6. distribute-frac-neg 95.9%

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

      7. distribute-frac-neg2 95.9%

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

      8. remove-double-neg 95.9%

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

      9. div-sub 95.9%

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

      10. *-inverses 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 70.9%

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

      1. mul-1-neg 70.9%

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

      2. distribute-frac-neg2 70.9%

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

      3. associate-*r/ 70.3%

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

   7. Simplified 70.3%

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

   if -205 < z < 1.4e-77

   1. Initial program 77.6%

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

      1. remove-double-neg 77.6%

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

      2. distribute-frac-neg2 77.6%

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

      3. distribute-frac-neg 77.6%

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

      4. distribute-rgt-neg-in 77.6%

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

      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%

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

      8. remove-double-neg 100.0%

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

      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 81.9%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -205 \lor \neg \left(z \leq 1.4 \cdot 10^{-77}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.4) (/ (* z (- x)) y) (if (<= z 7.2e-78) x (* x (/ z (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4) {
		tmp = (z * -x) / y;
	} else if (z <= 7.2e-78) {
		tmp = x;
	} else {
		tmp = x * (z / -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 <= (-1.4d0)) then
        tmp = (z * -x) / y
    else if (z <= 7.2d-78) then
        tmp = x
    else
        tmp = x * (z / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.4) {
		tmp = (z * -x) / y;
	} else if (z <= 7.2e-78) {
		tmp = x;
	} else {
		tmp = x * (z / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.4:
		tmp = (z * -x) / y
	elif z <= 7.2e-78:
		tmp = x
	else:
		tmp = x * (z / -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.4)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	elseif (z <= 7.2e-78)
		tmp = x;
	else
		tmp = Float64(x * Float64(z / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.4)
		tmp = (z * -x) / y;
	elseif (z <= 7.2e-78)
		tmp = x;
	else
		tmp = x * (z / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.4], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 7.2e-78], x, N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3999999999999999

   1. Initial program 88.2%

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

      1. remove-double-neg 88.2%

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

      2. distribute-frac-neg2 88.2%

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

      3. distribute-frac-neg 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

      5. associate-/l* 95.4%

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

      6. distribute-frac-neg 95.4%

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

      7. distribute-frac-neg2 95.4%

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

      8. remove-double-neg 95.4%

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

      9. div-sub 95.4%

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

      10. *-inverses 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. associate-*r/ 78.2%

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

      2. associate-*r* 78.2%

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

      3. mul-1-neg 78.2%

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

   7. Simplified 78.2%

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

   if -1.3999999999999999 < z < 7.2000000000000005e-78

   1. Initial program 77.6%

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

      1. remove-double-neg 77.6%

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

      2. distribute-frac-neg2 77.6%

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

      3. distribute-frac-neg 77.6%

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

      4. distribute-rgt-neg-in 77.6%

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

      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%

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

      8. remove-double-neg 100.0%

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

      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 81.9%

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

   if 7.2000000000000005e-78 < z

   1. Initial program 86.5%

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

      1. remove-double-neg 86.5%

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

      2. distribute-frac-neg2 86.5%

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

      3. distribute-frac-neg 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

      5. associate-/l* 96.3%

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

      6. distribute-frac-neg 96.3%

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

      7. distribute-frac-neg2 96.3%

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

      8. remove-double-neg 96.3%

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

      9. div-sub 96.3%

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

      10. *-inverses 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-frac-neg2 65.2%

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

      3. associate-*r/ 67.5%

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

   7. Simplified 67.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -28:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -28.0) (/ z (/ y (- x))) (if (<= z 1.4e-77) x (* x (/ z (- y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -28.0) {
		tmp = z / (y / -x);
	} else if (z <= 1.4e-77) {
		tmp = x;
	} else {
		tmp = x * (z / -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 <= (-28.0d0)) then
        tmp = z / (y / -x)
    else if (z <= 1.4d-77) then
        tmp = x
    else
        tmp = x * (z / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -28.0) {
		tmp = z / (y / -x);
	} else if (z <= 1.4e-77) {
		tmp = x;
	} else {
		tmp = x * (z / -y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -28.0:
		tmp = z / (y / -x)
	elif z <= 1.4e-77:
		tmp = x
	else:
		tmp = x * (z / -y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -28.0)
		tmp = Float64(z / Float64(y / Float64(-x)));
	elseif (z <= 1.4e-77)
		tmp = x;
	else
		tmp = Float64(x * Float64(z / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -28.0)
		tmp = z / (y / -x);
	elseif (z <= 1.4e-77)
		tmp = x;
	else
		tmp = x * (z / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -28.0], N[(z / N[(y / (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-77], x, N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -28

   1. Initial program 88.2%

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

      1. remove-double-neg 88.2%

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

      2. distribute-frac-neg2 88.2%

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

      3. distribute-frac-neg 88.2%

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

      4. distribute-rgt-neg-in 88.2%

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

      5. associate-/l* 95.4%

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

      6. distribute-frac-neg 95.4%

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

      7. distribute-frac-neg2 95.4%

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

      8. remove-double-neg 95.4%

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

      9. div-sub 95.4%

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

      10. *-inverses 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 78.2%

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

      1. associate-*r/ 78.2%

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

      2. associate-*r* 78.2%

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

      3. mul-1-neg 78.2%

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

   7. Simplified 78.2%

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

      1. div-inv 78.1%

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

      2. *-commutative 78.1%

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

      3. associate-*l* 73.7%

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

      4. add-sqr-sqrt 34.4%

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

      5. sqrt-unprod 29.4%

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

      6. sqr-neg 29.4%

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

      7. sqrt-unprod 0.7%

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

      8. add-sqr-sqrt 1.3%

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

      9. *-commutative 1.3%

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

      10. associate-*l/ 1.3%

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

      11. *-un-lft-identity 1.3%

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

   9. Applied egg-rr 1.3%

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

       1. associate-*r/ 1.2%

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

       2. add-sqr-sqrt 0.7%

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

       3. sqrt-unprod 33.3%

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

       4. sqr-neg 33.3%

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

       5. sqrt-unprod 39.9%

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

       6. add-sqr-sqrt 78.2%

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

       7. clear-num 78.1%

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

       8. metadata-eval 78.1%

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

       9. distribute-neg-frac 78.1%

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

       10. associate-/l/ 73.9%

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

       11. frac-2neg 73.9%

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

       12. associate-/r/ 73.7%

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

       13. associate-*l/ 73.9%

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

       14. neg-mul-1 73.9%

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

   11. Applied egg-rr 73.9%

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

   if -28 < z < 1.4e-77

   1. Initial program 77.6%

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

      1. remove-double-neg 77.6%

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

      2. distribute-frac-neg2 77.6%

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

      3. distribute-frac-neg 77.6%

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

      4. distribute-rgt-neg-in 77.6%

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

      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%

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

      8. remove-double-neg 100.0%

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

      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 81.9%

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

   if 1.4e-77 < z

   1. Initial program 86.5%

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

      1. remove-double-neg 86.5%

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

      2. distribute-frac-neg2 86.5%

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

      3. distribute-frac-neg 86.5%

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

      4. distribute-rgt-neg-in 86.5%

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

      5. associate-/l* 96.3%

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

      6. distribute-frac-neg 96.3%

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

      7. distribute-frac-neg2 96.3%

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

      8. remove-double-neg 96.3%

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

      9. div-sub 96.3%

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

      10. *-inverses 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 65.2%

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

      1. mul-1-neg 65.2%

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

      2. distribute-frac-neg2 65.2%

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

      3. associate-*r/ 67.5%

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

   7. Simplified 67.5%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -28:\\ \;\;\;\;\frac{z}{\frac{y}{-x}}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.1% 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 83.2%

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

   1. remove-double-neg 83.2%

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

   2. distribute-frac-neg2 83.2%

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

   3. distribute-frac-neg 83.2%

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

   4. distribute-rgt-neg-in 83.2%

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

   5. associate-/l* 97.6%

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

   6. distribute-frac-neg 97.6%

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

   7. distribute-frac-neg2 97.6%

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

   8. remove-double-neg 97.6%

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

   9. div-sub 97.7%

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

   10. *-inverses 97.7%

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

3. Simplified 97.7%

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

5. Taylor expanded in z around 0 50.6%

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

Developer Target 1: 96.3% 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 2024137 
(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))