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

Percentage Accurate: 84.6% → 95.8%

Time: 7.6s

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: 84.6% 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: 95.8% 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 83.4%

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

   1. remove-double-neg 83.4%

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

   2. distribute-frac-neg2 83.4%

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

   3. distribute-frac-neg 83.4%

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

   4. distribute-rgt-neg-in 83.4%

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

   5. associate-/l* 98.4%

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

   6. distribute-frac-neg 98.4%

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

   7. distribute-frac-neg2 98.4%

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

   8. remove-double-neg 98.4%

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

   9. div-sub 98.4%

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

   10. *-inverses 98.4%

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

3. Simplified 98.4%

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

Alternative 2: 70.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+76} \lor \neg \left(z \leq 1.75 \cdot 10^{-67}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.6e+76) (not (<= z 1.75e-67))) (* x (/ z (- y))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.6e+76) || !(z <= 1.75e-67)) {
		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 <= (-4.6d+76)) .or. (.not. (z <= 1.75d-67))) 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 <= -4.6e+76) || !(z <= 1.75e-67)) {
		tmp = x * (z / -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.6e+76) or not (z <= 1.75e-67):
		tmp = x * (z / -y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.6e+76) || !(z <= 1.75e-67))
		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 <= -4.6e+76) || ~((z <= 1.75e-67)))
		tmp = x * (z / -y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.6e+76], N[Not[LessEqual[z, 1.75e-67]], $MachinePrecision]], N[(x * N[(z / (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000002e76 or 1.75e-67 < z

   1. Initial program 88.4%

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

      1. remove-double-neg 88.4%

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

      2. distribute-frac-neg2 88.4%

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

      3. distribute-frac-neg 88.4%

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

      4. distribute-rgt-neg-in 88.4%

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

      5. associate-/l* 96.8%

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

      6. distribute-frac-neg 96.8%

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

      7. distribute-frac-neg2 96.8%

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

      8. remove-double-neg 96.8%

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

      9. div-sub 96.8%

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

      10. *-inverses 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 70.8%

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

      1. mul-1-neg 70.8%

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

      2. distribute-frac-neg2 70.8%

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

      3. associate-*r/ 70.7%

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

   7. Simplified 70.7%

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

   if -4.60000000000000002e76 < z < 1.75e-67

   1. Initial program 78.7%

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

      1. remove-double-neg 78.7%

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

      2. distribute-frac-neg2 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. distribute-rgt-neg-in 78.7%

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

      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 78.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+76} \lor \neg \left(z \leq 1.75 \cdot 10^{-67}\right):\\ \;\;\;\;x \cdot \frac{z}{-y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.8e+76)
   (/ (* z (- x)) y)
   (if (<= z 1.75e-67) x (/ x (/ y (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.8e+76) {
		tmp = (z * -x) / y;
	} else if (z <= 1.75e-67) {
		tmp = x;
	} 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 (z <= (-4.8d+76)) then
        tmp = (z * -x) / y
    else if (z <= 1.75d-67) then
        tmp = x
    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 (z <= -4.8e+76) {
		tmp = (z * -x) / y;
	} else if (z <= 1.75e-67) {
		tmp = x;
	} else {
		tmp = x / (y / -z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.8e+76:
		tmp = (z * -x) / y
	elif z <= 1.75e-67:
		tmp = x
	else:
		tmp = x / (y / -z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.8e+76)
		tmp = Float64(Float64(z * Float64(-x)) / y);
	elseif (z <= 1.75e-67)
		tmp = x;
	else
		tmp = Float64(x / Float64(y / Float64(-z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.8e+76)
		tmp = (z * -x) / y;
	elseif (z <= 1.75e-67)
		tmp = x;
	else
		tmp = x / (y / -z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.8e+76], N[(N[(z * (-x)), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.75e-67], x, N[(x / N[(y / (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e76

   1. Initial program 91.7%

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

      1. remove-double-neg 91.7%

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

      2. distribute-frac-neg2 91.7%

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

      3. distribute-frac-neg 91.7%

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

      4. distribute-rgt-neg-in 91.7%

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

      5. associate-/l* 94.4%

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

      6. distribute-frac-neg 94.4%

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

      7. distribute-frac-neg2 94.4%

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

      8. remove-double-neg 94.4%

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

      9. div-sub 94.4%

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

      10. *-inverses 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around inf 83.7%

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

      1. associate-*r/ 83.7%

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

      2. associate-*r* 83.7%

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

      3. mul-1-neg 83.7%

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

   7. Simplified 83.7%

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

   if -4.8e76 < z < 1.75e-67

   1. Initial program 78.7%

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

      1. remove-double-neg 78.7%

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

      2. distribute-frac-neg2 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. distribute-rgt-neg-in 78.7%

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

      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 78.9%

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

   if 1.75e-67 < z

   1. Initial program 87.1%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

   4. Applied egg-rr 87.0%

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

      1. clear-num 87.1%

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

      2. inv-pow 87.1%

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

      3. associate-/l* 97.7%

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

   6. Applied egg-rr 97.7%

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

      1. unpow-1 97.7%

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

      2. associate-/r* 97.6%

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

      3. div-sub 97.6%

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

      4. *-inverses 97.6%

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

   8. Simplified 97.6%

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

      1. unpow-1 97.6%

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

      2. div-inv 97.5%

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

      3. associate-/r* 97.6%

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

      4. clear-num 97.7%

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

      5. /-rgt-identity 97.7%

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

      6. frac-2neg 97.7%

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

      7. metadata-eval 97.7%

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

      8. sub-neg 97.7%

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

      9. distribute-neg-in 97.7%

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

      10. metadata-eval 97.7%

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

      11. distribute-neg-frac2 97.7%

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

      12. distribute-frac-neg 97.7%

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

      13. frac-2neg 97.7%

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

   10. Applied egg-rr 97.7%

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

   11. Taylor expanded in z around inf 67.1%

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

       1. associate-*r/ 67.1%

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

       2. neg-mul-1 67.1%

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

   13. Simplified 67.1%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{z \cdot \left(-x\right)}{y}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{-z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.5e-76) x (if (<= y 8.4e-77) (* z (/ (- x) y)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.5e-76) {
		tmp = x;
	} else if (y <= 8.4e-77) {
		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 <= (-8.5d-76)) then
        tmp = x
    else if (y <= 8.4d-77) 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 <= -8.5e-76) {
		tmp = x;
	} else if (y <= 8.4e-77) {
		tmp = z * (-x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8.5e-76:
		tmp = x
	elif y <= 8.4e-77:
		tmp = z * (-x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.5e-76)
		tmp = x;
	elseif (y <= 8.4e-77)
		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 <= -8.5e-76)
		tmp = x;
	elseif (y <= 8.4e-77)
		tmp = z * (-x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.5e-76], x, If[LessEqual[y, 8.4e-77], N[(z * N[((-x) / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -8.50000000000000038e-76 or 8.40000000000000061e-77 < y

   1. Initial program 79.5%

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

      1. remove-double-neg 79.5%

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

      2. distribute-frac-neg2 79.5%

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

      3. distribute-frac-neg 79.5%

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

      4. distribute-rgt-neg-in 79.5%

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

      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 72.9%

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

   if -8.50000000000000038e-76 < y < 8.40000000000000061e-77

   1. Initial program 91.0%

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

      1. remove-double-neg 91.0%

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

      2. distribute-frac-neg2 91.0%

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

      3. distribute-frac-neg 91.0%

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

      4. distribute-rgt-neg-in 91.0%

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

      5. associate-/l* 95.5%

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

      6. distribute-frac-neg 95.5%

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

      7. distribute-frac-neg2 95.5%

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

      8. remove-double-neg 95.5%

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

      9. div-sub 95.5%

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

      10. *-inverses 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around inf 79.1%

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

      1. mul-1-neg 79.1%

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

      2. distribute-frac-neg2 79.1%

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

      3. *-commutative 79.1%

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

      4. associate-/l* 80.6%

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

   7. Simplified 80.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.4 \cdot 10^{-77}:\\ \;\;\;\;z \cdot \frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 5e+56) x (* y (/ x y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e+56) {
		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 <= 5d+56) 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 <= 5e+56) {
		tmp = x;
	} else {
		tmp = y * (x / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 5e+56:
		tmp = x
	else:
		tmp = y * (x / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 5e+56)
		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 <= 5e+56)
		tmp = x;
	else
		tmp = y * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 5e+56], x, N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.00000000000000024e56

   1. Initial program 87.2%

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

      1. remove-double-neg 87.2%

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

      2. distribute-frac-neg2 87.2%

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

      3. distribute-frac-neg 87.2%

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

      4. distribute-rgt-neg-in 87.2%

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

      5. associate-/l* 98.1%

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

      6. distribute-frac-neg 98.1%

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

      7. distribute-frac-neg2 98.1%

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

      8. remove-double-neg 98.1%

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

      9. div-sub 98.1%

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

      10. *-inverses 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in z around 0 54.2%

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

   if 5.00000000000000024e56 < x

   1. Initial program 66.4%

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

   3. Taylor expanded in y around inf 23.4%

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

      1. *-commutative 23.4%

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

      2. associate-/l* 58.9%

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

   5. Applied egg-rr 58.9%

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

Alternative 6: 50.8% 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 83.4%

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

   1. remove-double-neg 83.4%

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

   2. distribute-frac-neg2 83.4%

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

   3. distribute-frac-neg 83.4%

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

   4. distribute-rgt-neg-in 83.4%

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

   5. associate-/l* 98.4%

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

   6. distribute-frac-neg 98.4%

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

   7. distribute-frac-neg2 98.4%

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

   8. remove-double-neg 98.4%

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

   9. div-sub 98.4%

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

   10. *-inverses 98.4%

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

3. Simplified 98.4%

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

5. Taylor expanded in z around 0 54.7%

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

Developer Target 1: 95.8% 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 2024180 
(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))